Resonator electrode configuration for avoiding capacitive feedthrough of a vibrating beam accelerometer

Abstract

This invention is entitled "Resonator electrode configuration for avoiding capacitive feedthrough of a vibrating beam accelerometer." This disclosure describes techniques to configure the capacitive comb fingers of an accelerometer resonator with discrete electrodes having a drive electrode and at least two sense electrodes. Routing of electrical signals is configured to produce approximately equal parasitic feedthrough capacitances. The sense electrodes can be placed on opposite sides of the moving resonator beam so that the magnitude of the capacitive change with respect to displacement (e.g., dC / dx) is approximately equal and the sign is opposite. The arrangement can result in sense currents of opposite sign and feedthrough currents of the same sign. The sense outputs from the resonator can be connected to a differential amplifier so that the difference in output currents can mitigate the effects of the feedthrough currents and cancel the parasitic feedthrough capacitances. Parasitic feedthrough capacitances can result in increased accelerometer noise and reduced bias stability.

Description

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 62 / 932,397, filed November 7, 2019, and U.S. Provisional Patent Application No. 62 / 932,298, filed November 7, 2019, the entire contents of each of which are incorporated herein by reference. Technical Field

[0002] This disclosure relates to a vibrating beam accelerometer. Background Technology

[0003] An accelerometer functions by detecting the displacement of a test mass under inertial force. In one example, the accelerometer can detect the displacement of the test mass by measuring the frequency change of a resonator connected between the test mass and a support base. The resonator can be designed to change the frequency proportional to the load applied to the resonator by the test mass under acceleration. The resonator can be electrically coupled to a signal generating circuit that forms an oscillator, causing the resonator to vibrate, and in some examples, to vibrate at the resonant frequency of the resonator. Summary of the Invention

[0004] Generally, this disclosure provides techniques for improving the functionality of a vibrating beam accelerometer (VBA). In one example, this disclosure describes a technique for simultaneously implementing an underdamped resonator using a test mass for a damped accelerometer. In an example of an in-plane microelectromechanical system (MEMS) VBA, the test mass may include one or more damping combs, each including one or more sets of movable comb fingers attached to the test mass. The movable comb fingers may intersect with anchor comb fingers attached to a fixed geometry. When the MEMS die is placed in a pressure chamber of a package containing pressure above vacuum, these damping comb fingers can provide air damping for the test mass. In some examples, the MEMS die may be placed in a ceramic package containing pressure of approximately 1 Torr. The geometry of the damping comb minimizes the air gap and maximizes the overlap area between the movable comb fingers and the anchor comb fingers. The geometry of the resonator in this VBA can be configured to avoid air damping.

[0005] In other examples, this disclosure describes a technique for configuring the capacitive comb fingers of an accelerometer resonator as discrete electrodes with a drive electrode and at least two sensing electrodes. The technique also describes the routing of electrical signals on the die and on the analog electronics board, designed to produce substantially equal parasitic feedthrough capacitances. The at least two sensing electrodes can be placed on opposite sides of the moving resonator beam such that the magnitudes of capacitance changes relative to displacement (e.g., dC / dx) are substantially equal and opposite in sign. This can result in sensing currents with opposite signs and cause feedthrough currents to have the same sign. The sensing output from the resonator can be connected to a differential front-end amplifier (such as a transimpedance or charge amplifier) ​​that handles the difference in the output current. Handling the difference in the output current mitigates the effects of the feedthrough current and eliminates parasitic feedthrough capacitance. Parasitic feedthrough capacitance can lead to increased accelerometer noise and reduced bias stability.

[0006] In other examples, this disclosure describes a vibrating beam accelerometer (VBA) device comprising: a resonator including: a resonator beam; a drive electrode; and a first sensing electrode and a second sensing electrode, wherein: the first sensing electrode is located on a first side of the resonator beam, and the second sensing electrode is located on a second side of the resonator beam opposite to the first side, such that the magnitude of a first capacitance change (dC1 / dx) of the first sensing electrode relative to displacement is approximately equal to and opposite in sign to the magnitude of a second capacitance change (dC2 / dx) of the second sensing electrode relative to displacement; and an electrical signal routing comprising: a drive signal path coupled to the drive electrode; a first sensing signal path coupled to the first sensing electrode; and a second sensing signal path coupled to the second sensing electrode. The electrical signal routing is configured to generate: a first parasitic capacitance between the drive signal path and the first sensing signal path that generates a first parasitic feedthrough current; and a second parasitic capacitance between the drive signal path and the second sensing signal path that generates a second parasitic feedthrough current, such that the magnitudes of the first parasitic feedthrough current and the second parasitic feedthrough current are approximately equal.

[0007] In other examples, this disclosure describes a method comprising: receiving, by processing circuitry, one or more electrical signals from a vibrating beam accelerometer (VBA) indicating the frequencies of a first resonator beam and a second resonator beam, wherein the VBA includes: a resonator comprising: a first resonator beam; a drive electrode; and a first sensing electrode and a second sensing electrode, wherein: the first sensing electrode is located on a first side of the resonator beam, and the second sensing electrode is located on a second side of the resonator beam opposite to the first side, such that the magnitude of a first capacitance change (dC1 / dx) of the first sensing electrode relative to displacement is substantially equal to and opposite in sign to the magnitude of a second capacitance change (dC2 / dx) of the second sensing electrode relative to displacement; and electrical signal routing comprising: a drive signal path, the drive signal... A path is coupled to a driving electrode; a first sensing signal path is coupled to a first sensing electrode; and a second sensing signal path is coupled to a second sensing electrode, wherein the electrical signal routing is configured to generate: a first parasitic capacitance between the driving signal path and the first sensing signal path that generates a first parasitic feedthrough current; and a second parasitic capacitance between the driving signal path and the second sensing signal path that generates a second parasitic feedthrough current, such that the magnitudes of the first parasitic feedthrough current and the second parasitic feedthrough current are approximately equal; and the frequency of the first resonator beam and the frequency of the second resonator beam are determined by the processing circuit based on one or more electrical signals; and the acceleration of the VBA is calculated by the processing circuit based on the frequency of the first resonator beam and the frequency of the second resonator beam.

[0008] In other examples, this disclosure describes a system for determining acceleration, the system comprising: processing circuitry coupled to and configured to cause the resonator drive circuitry to output a resonator drive signal; and a vibrating beam accelerometer (VBA) device comprising: a resonator configured to receive the resonator drive signal, the resonator comprising: a resonator beam; a drive electrode; and a first sensing electrode and a second sensing electrode, wherein: the first sensing electrode is located on a first side of the resonator beam, and the second sensing electrode is located on a second side of the resonator beam opposite to the first side, such that the magnitude of a first capacitance change (dC1 / dx) of the first sensing electrode relative to displacement is related to the magnitude of the second sensing electrode relative to displacement. The magnitudes of the second capacitance change (dC2 / dx) are approximately equal and opposite in sign; and the electrical signal routing includes: a drive signal path coupled to a drive electrode; a first sensing signal path coupled to a first sensing electrode; and a second sensing signal path coupled to a second sensing electrode, wherein the electrical signal routing is configured to generate: a first parasitic capacitance between the drive signal path and the first sensing signal path that generates a first parasitic feedthrough current; and a second parasitic capacitance between the drive signal path and the second sensing signal path that generates a second parasitic feedthrough current, such that the magnitudes of the first parasitic feedthrough current and the second parasitic feedthrough current are approximately equal. Attached Figure Description

[0009] Figure 1 This is a conceptual diagram showing a suspended VBA with a supporting flexure, an X-direction resonator, and a damping comb.

[0010] Figure 2 This is a conceptual diagram showing a cross-sectional view of a suspended VBA with a supporting flexure and an X-direction resonator.

[0011] Figure 3A This is a block diagram illustrating a system including a suspended VBA according to one or more techniques of this disclosure.

[0012] Figure 3B This is a block diagram illustrating an accelerometer system according to one or more technologies of this disclosure.

[0013] Figure 4 This is a conceptual diagram illustrating an example of resonator electrode placement and electrical signal routing to avoid the effects of parasitic feedthrough capacitance on accelerometer performance.

[0014] Figure 5A and Figure 5B This is a schematic diagram illustrating an exemplary MEMS VBA configured with a single sensing electrode.

[0015] Figure 6A and Figure 6BThis is a schematic diagram illustrating an exemplary MEMS VBA configured with two sensing electrodes according to one or more techniques of this disclosure.

[0016] Figure 7A This is a conceptual diagram illustrating a first resonator with an additional mass block according to one or more techniques of this disclosure.

[0017] Figure 7B This illustrates one or more technologies according to this disclosure. Figure 7A A conceptual diagram of a portion of the first resonator, which includes an additional mass block.

[0018] Figure 8A This is a conceptual diagram illustrating a second resonator forming a gap according to one or more techniques according to this disclosure.

[0019] Figure 8B This illustrates one or more technologies according to this disclosure. Figure 5A A conceptual diagram of a portion of a second resonator, including the gap.

[0020] Figure 9 It is a graph showing a first graph and a second graph according to one or more techniques of the present disclosure, the first graph representing a quadratic nonlinear coefficient as a function of the position of the added mass, and the second graph representing the zero-acceleration resonant frequency difference as a function of the position of the added mass.

[0021] Figure 10 This is a flowchart illustrating exemplary operations for determining VBA acceleration according to one or more techniques of this disclosure. Detailed Implementation

[0022] The technology disclosed herein can be incorporated into various VBAs. For example, the technology described in U.S. Patent Application 16 / 041,244 (whose entire contents are incorporated herein by reference) regarding the planar geometry and the single primary mechanical anchor between the support base and the VBA can be combined with the technology disclosed herein.

[0023] Figure 1 This is a conceptual diagram showing a suspended VBA with a supporting flexure and an X-direction resonator. Figure 1 This is a top view showing the VBA 30 from the anchor 14 to the support base, but... Figure 1 The support base is not shown. The VBA 30 includes a suspended test mass 32 connected at the hinge flexure 22 to the anchor 14 and the resonator connection structure 16, the suspended test mass having a damping comb 40 and resonators 18A and 18B. Figure 1A section A-A' extending along the long axis of the resonator connection structure 16 and passing through the anchor 14 is also shown. In this disclosure, the resonator connection structure 16 may also be referred to as the rigid anchor connection 16.

[0024] The suspended test mass 32 includes a supporting flexure and is connected to the resonator connection structure 16 at the anchor 14 via a hinged flexure 22. The hinged flexure 22 suspends the test mass at the anchor 14, and the point where the hinged flexure 22 connects to the anchor 14 is the rotation center of the test mass 32. The left resonator 18A and the right resonator 18B are connected to the same main anchor 14 via the resonator connection structure 16. The resonators 18A and 18B are connected to the test mass 12 at a distance r1 from the rotation center of the test mass 32. The distance r2 from the center of mass 24 of the test mass 12 to the rotation center of the test mass 12 is the same. The arrangement of the VBA 30 causes the inertial force of the test mass 12 on the release beams of the resonator beams 19A and 19B to be amplified by a leverage ratio r2 / r1.

[0025] In the example Figure 1 In this embodiment, VBA 30 can be implemented as an in-plane microelectromechanical system (MEMS) VBA. The test mass block 32 may include one or more damping combs 40, each comprising one or more sets of movable comb fingers 42 attached to the test mass block 32. The movable comb fingers 42 may intersect with anchoring comb fingers 44 attached to a fixed geometry (such as an anchor 46). These damping comb fingers 42 and 44 lie in the same plane as the test mass block 32 and can provide air damping to the test mass block 32 when the MEMS die is placed in a package containing pressure above vacuum. In some examples, the MEMS die may be placed in a ceramic package containing an internal pressure of approximately 1 Torr. Pressure variations can alter the degree of damping. In this disclosure, "movable comb finger 42" may be referred to as "rotor comb finger 42." Additionally, "anchoring comb finger 44" may be referred to as "stator comb finger 44."

[0026] In this disclosure, air damping may include damping caused by two surfaces sliding over each other, such as coueter damping. In other examples, air damping may include two surfaces close to each other, such as extruded membrane damping. In some examples, one type of air damping may have a greater effect than other types of air damping, and may depend on the VBA geometry.

[0027] The geometry of the damping comb 40 minimizes the air gap and maximizes the overlap area between the movable comb finger 42 and the anchoring comb finger 44. For example... Figure 1As shown, the first comb finger in the movable comb finger is adjacent to the first and second comb fingers in the anchor comb finger. The overlapping portion has a linear distance. The linear distance is the sum of a first length and a second length. The first length is the linear distance at which the first edge of the first comb finger in the movable comb finger overlaps with the first edge of the first comb finger in the anchor comb finger. The second length is the linear distance at which the second edge of the first comb finger in the movable comb finger overlaps with the first edge of the second comb finger in the anchor comb finger. Figure 1 The example shows six damping combs. However, in other examples, the VBA may include more or fewer damping combs. More damping combs result in a larger overlap and therefore a longer bus linear distance. A longer bus linear distance results in greater damping. Similarly, more fingers per damping comb result in a longer bus linear distance and greater damping. Movable and anchoring comb fingers can be configured with multiple widths in the X direction. Thinner (e.g., more slender) fingers result in more fingers, a larger bus linear distance, and greater damping. Additionally, movable and anchoring comb fingers can be configured with multiple lengths in the Y direction. Longer fingers result in a larger bus linear distance and greater damping. Because the quality factor depends on the damping as well as the mass and stiffness of the VBA 30, designers can consider the desired amount of damping and the mechanical and structural strength of the VBA 30 when selecting the geometry of the damping comb 40.

[0028] The test mass block 32 may include one or more support flexures to increase the stiffness of the test mass block 32 in the out-of-plane (z) direction. In other words, the support flexures (e.g., flexure 33) coupled to the test mass block 32 are configured to restrict out-of-plane movement of the suspended test mass block relative to an XY plane parallel to the test mass block 32 and the resonator connection structure 16. These flexures are configured to be significantly more flexible in the in-plane (x and y) directions compared to a rigid resonator connection structure or compared to the axial stiffness of the resonator. For example, flexure 33 includes connections to the support base similar to those of the main anchors 14 and 46. Figure 1 An anchoring portion (not shown). The flexure 33 may include a flexible portion 36C connecting the anchoring portion 33 and the test mass 32. The flexible portion 36C may have the same or similar material as the test mass 32. The configuration of one or more supporting flexures can reduce out-of-plane movement while avoiding bias caused by forces applied to the accelerometer mechanism (e.g., the test mass 32 and resonators 18A and 18B), which may be caused by CTE mismatch between the base and the accelerometer mechanism.

[0029] The inspection quality block 32 may include additional support flexures, such as flexures having anchor portions 34A and 34B and flexible portions 36A and 36B. As described above with respect to flexure 33, the flexible portions 36A and 36B may have the same or similar material as the inspection quality block 32. Figure 1 The positions of the anchoring portions 34A and 34B, and the shapes and configurations of the flexible portions 36A and 36B shown, are merely one exemplary technique for providing support flexures to reinforce the out-of-plane (z) movement of the test mass block 32. In other examples, the flexible portions 36A and 36B may have different shapes, such as straight beams or S-shapes. In other examples, the VBA 30 may have more or fewer support flexures. The anchoring portions of the support flexures of this disclosure will not exert significant forces on the test mass block 32, so the mechanism of the VBA 30 will still be primarily connected to the support base via a single anchoring region (e.g., anchor 14). Advantages of the geometry of the VBA 30 may include a reduction in bias errors that might otherwise be caused by thermal expansion mismatch between the glass substrate (support base) and the silicon mechanism (e.g., the suspended test mass block 32).

[0030] Using a single primary mechanical anchor 14 can reduce or prevent bias errors that can be caused by external mechanical forces applied to the circuit board, package, and / or substrate (containing the accelerometer mechanism). Since the sources of these forces may be unavoidable (e.g., thermal expansion mismatch between the substrate and the mechanism), the geometry of the VBA of this disclosure mechanically isolates sensitive components. Another advantage may include reduced cost and complexity by achieving mechanical isolation within the MEMS mechanism, which avoids the need for additional manufacturing steps or components, such as discrete isolation stages.

[0031] The damping comb 40 is an exemplary technique for simultaneously implementing an underdamped resonator by moving a test mass block in a damped accelerometer. The vibrating beam accelerometer (VBA) functions by applying an inertial force to the vibrating beam (also known as resonators 18A and 18B) using the test mass block, such that the applied acceleration can be measured as a change in the resonant frequency of the vibrating beam.

[0032] A high quality factor (Q) can have the beneficial effect of mitigating the phase shift inherent in resonator control electronics. This phase shift can lead to a frequency shift, which ultimately manifests as bias error. A large quality factor (Q), i.e., essentially underdamped, also reduces the applied voltage required to achieve a specific displacement amplitude. However, to minimize vibration rectification error (VRE), the motion of the test mass must be substantially damped, and in some examples critically damped, i.e., returned to equilibrium as quickly as possible without oscillation. Without sufficient test mass damping, the accelerometer output can exhibit unacceptable bias error in the presence of ambient vibration.

[0033] Compared to the damping comb 40, the geometries of the resonators 18A and 18B of the VBA 30 of this disclosure can be designed to avoid air damping. The geometry and voltage division of the components of the MEMS VBA of this disclosure allow the underdamped resonator to have a relatively high quality factor Q, but with a damped check mass block, making the check mass block Q relatively low compared to the Q of the resonator. For example, the reduced total linear distance of the comb on the resonator 18 can configure the relative Q between the comb 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 finger 42 and the stator comb finger 44 of the damping comb 40 can also affect the relative Q.

[0034] The 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 overdamped system, the system returns to equilibrium without oscillation. A critically damped system returns to equilibrium as quickly as possible without oscillation. An underdamped system can oscillate (at a decreasing frequency compared to the undamped case), where the amplitude gradually decreases to zero. The quality factor can be written as:

[0035] Q = E / [-dE / dθ]

[0036] When dE / dθ is written as (dE / dt) / (dθ / dt), the formula becomes:

[0037] Q = E / [-dE / dt / dθ / dt].

[0038] Since dE / dt is P (the dissipated power) and dθ / dt is the angular frequency ω, this can be written as:

[0039] Q = ωE / [-dE / dt] = ωE / P = ω (stored energy / dissipated power).

[0040] The frequency can be further described as follows: ω1 is the underdamped oscillation frequency (slightly smaller than the undamped frequency ω). o ):ω1 2 =ω o 2 -β 2 .

[0041] The techniques disclosed herein can be applied, for example, to microelectromechanical systems (MEMS) vibrating beam accelerometers (VBAs), representing one of several possible solutions capable of achieving the desired accelerometer performance. The techniques disclosed herein improve the basic operation of VBAs. In existing MEMS VBAs, the resonator can be substantially underdamped (where Q is in the range of 100 to possibly 100,000), which reduces the impact of phase shifts from control electronics on the closed-loop resonant frequency. As discussed above, the underdamped resonator contrasts with the secondary design goal of a damped check mass. These techniques provide a way to achieve an underdamped resonator (Q approximately 1000) while also damping the check mass, representing an advantage over other alternative solutions.

[0042] Alternative solutions exist for partial damping of the test mass, but some alternatives have drawbacks that limit the required combination of performance, cost, and size, weight, and power (SWaP). A first example of an alternative could be to seal both the test mass and the resonator in a full atmosphere. Full atmosphere solutions can be used for larger devices. However, the air damping of the resonator becomes excessive after the size is scaled down to the typical MEMS scale. Excessive air damping can limit the ability to be electrostatically driven and increase the device's susceptibility to phase errors from the control electronics.

[0043] A second alternative example could include sealing the test mass and the resonator in a separate cavity, such that the test mass is encapsulated in a full atmosphere while the resonator is encapsulated in a vacuum. This alternative example could significantly complicate device manufacturing and thus ultimately increase costs.

[0044] A third alternative could involve sealing the test mass and resonator under vacuum. This third alternative could mitigate vibration rectification errors by setting the test mass resonant frequency significantly higher than the ambient vibration frequency. Unfortunately, the available die size and minimum resonator beam width prevent this solution from becoming feasible. Under the current constraints, significantly increasing the test mass frequency results in a low scaling factor, which could ultimately lead to poor bias performance.

[0045] A fourth example could include sealing the test mass and resonator under vacuum. An active vibration-suppressing force rebalancing actuator could mitigate vibration rectification errors. Additional actuation electrodes could be included to counteract vibrations at high frequencies (>100Hz) while allowing the test mass to deflect at lower frequencies (<100Hz). This solution could be feasible, but it introduces additional complexity to both the mechanical equipment and auxiliary electronics, and assumes the introduction of costs.

[0046] Compared to existing technologies, the techniques disclosed herein provide a method for damping a test mass while making the resonator significantly underdamped. This damping is achieved through gas damping, eliminating the need for separate chambers for different pressures. Finally, the techniques disclosed herein enable navigation-grade accelerometers with reduced cost and SWaP to maintain bias repeatability in the presence of environmental vibrations. These techniques avoid separate pressure chambers and / or more complex auxiliary electronics, both of which can lead to higher costs.

[0047] Using voltage divider damping may include integrating the following features into VBA designs:

[0048] 1. The inspection mass block may have a large area defined by a small air gap (typically a few micrometers) between the inspection mass block and the anchoring geometry. Given sufficient gas pressure, this gap can generate air damping and ultimately reduce the Q of the inspection mass block's motion.

[0049] 2. The resonator can have only a small region that contributes to air damping, which enables a relatively high Q resonator.

[0050] 3. MEMS devices can be packaged under voltage divider conditions, which, combined with test mass block damping, results in a relatively high-Q resonator (Q approximately 100 or higher) and a low-Q test mass block (Q < 100).

[0051] In some examples, voltage divider techniques can be implemented within an in-plane MEMS VBA. For example... Figure 1 As shown, a test mass block 32, comprising multiple sets of movable comb fingers 42 intersecting with anchor comb fingers 44, can be attached to a fixed geometry portion 46 of the accelerometer. The fingers of these damping combs 40 provide air damping for the test mass block 32. To maximize damping, the air gap can be reduced while simultaneously maximizing the overlap area between comb fingers 42 and 44. Unlike the damping combs, the resonator can be configured to avoid air damping. The MEMS die is placed in a ceramic package containing approximately 1 Torr of pressure. This pressure division allows the resonator to have a relatively high Q (approximately 1000) but keeps the test mass block Q slightly damped (Q approximately 10).

[0052] In addition to in-plane MEMS VBAs, the same concept can be applied to out-of-plane MEMS VBAs. Such devices can utilize a parallel plate gap between a test mass and an anchoring geometry (rather than a cross-finger). The basic concept can be the same: air damping will dampen the test mass while giving the resonator a relatively high Q. A similar voltage division of approximately 1 Torr would likely result in adequate damping with respect to typical air gaps and device geometry.

[0053] It should be noted that the techniques disclosed herein can be applied to VBAs operated by different actuation methods. For example, piezoelectric actuation of the resonator can reduce the need for a small capacitive air gap within the resonator geometry. A larger capacitive air gap can achieve even greater differences between the resonator Q and the test mass Q. In some examples, the VBA can provide test mass damping via multiple sets of damping combs embedded within the test mass, but other geometries and configurations can theoretically achieve similar effects. In some examples, the damping combs can be attached to the sides of the test mass rather than embedded in the middle. For some designs, the edges of the test mass itself, with a sufficiently small air gap, may be sufficient to provide test mass damping.

[0054] Figure 2 This is a conceptual diagram showing a cross-sectional view of a suspended VBA with a supporting flexure and an X-direction resonator. Figure 2 This shows a structure extending downwards along the long axis of the resonator connection structure 16 and passing through the anchor 14. Figure 1 The section A-A' of VBA 30 is depicted in the figure. Figure 2 Chinese reference symbols and Figure 1 Parts with the same reference numerals have the same description, characteristics, and functions as described above. For example, VBA 50 includes a suspended test mass block 32 connected at anchor 14 to resonator connection structure 16. Figure 2 (Not shown in the image). Figure 2 Anchoring portions of anchoring combs 26C and 20C, as well as anchoring portions of supporting flexural members 34A and 34B, are also shown. Anchoring member 46 of damping comb 40 may also be mechanically connected to support base 36. Figure 2 (Not shown in the image).

[0055] Related to the above text Figure 1 Like the VBA 30, the VBA 50 can be fabricated using silicon and glass masks, such that both the test mass block 32 and the resonator connection structure 16 are primarily anchored to a single area, such as anchor 14. The silicon release mechanism of the VBA 50 can be attached to a support base 36, which can be a glass substrate, such as a quartz substrate or a silicon substrate. The test mass block 32 can also be attached to other anchoring areas (e.g., anchoring portions 34A and 34B) configured to allow the release of silicon portions (such as the test mass block 32 and the resonator beams 19A and 19B of resonators 18A and 18B). Figure 2 (not shown in the image) can move freely relative to the support base 36.

[0056] The support base 36 may include an encapsulation structure, such as structures 38A and 38B, that can surround the release portion of the VBA 30. In some examples, the VBA 30 may include a lower support base 36 and an upper support (not shown in FIG. 2). In some examples, an anchoring portion, such as anchor 14, may be mechanically connected to both the lower support base 36 and the upper support. The support base 36 may define a second plane that is also substantially parallel to the XY plane, which is different from the plane of the release portion of the VBA 30. The plane defined by the release portion of the VBA 30 (e.g., resonator beams 19A-19B and test mass block 32) may be substantially parallel to the second plane defined by the support base 36. As stated above regarding Figure 1 The air gap between the plane of the test mass block and the plane of the support base 36 allows the silicon portion (such as the test mass block) to move freely relative to the substrate.

[0057] The resonator connection structure 16 can be configured to be more rigid than the resonator. The rigid structure of the resonator connection structure 16 connects to the resonator and branches back to the main mechanical anchor 14, which connects 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 supports the resonator in a plane (e.g., x and y) direction. In some examples, the resonator connection structure 16 may be an order of magnitude stiffer than the resonator beams 19A-19B. The single main anchor 14 allows the mechanical connection of the release portion of the VBA 30 to thermally expand at different rates or directions with respect to the support base 36, without being constrained by other connections to the support base 36 that could lead to bias and inaccuracies.

[0058] The support base 36 may include a glass substrate (deposited into the glass substrate). Figure 2 Metal layers (not shown) define wires connecting silicon electrodes to wire bonding pads. In some examples, the support base 36 may include bonding pads and other metal structures (e.g., as indicated by arrows from 36) on the bottom surface of the support base 36, such as conductive paths 37A and 37B. In some examples, the support base 36 may include metal layers on the top surface (e.g., on the surface opposite the bottom surface), and in other examples, the support base 36 may include an intermediate metal layer between the top and bottom surfaces. Figure 2 (Not shown in the image). In some examples, these metal layers may be electrically connected to each other via through-holes or other types of connections through the support base 36. In some examples, the wires may also be defined by conductive materials other than metals. As mentioned above... Figure 1 The metal layer or other conductive material may define electrical paths for carrying signals to and from the VBA 30, such as conductive paths 37A and 37B.

[0059] As mentioned above Figure 1 Each of the one or more resonators may include a resonator beam with a release comb (e.g., 19A) and an anchoring comb (e.g., 20C and 26C). Figure 2 As shown, the anchoring combs and the anchoring portions of 20C and 26C extend from the plane of the support base 36 to the plane of the release portion of the VBA 30. The comb portions of the anchoring combs 20C and 26C are supported in the same plane as the resonator beams 19A-19B and the test mass blocks 12 and 32, as described above. Figure 1 As stated above.

[0060] Figure 3A This is a functional block diagram illustrating a system including a suspended VBA according to one or more techniques of this disclosure. The functional blocks of system 100 are merely one example of a system that may include VBA according to this disclosure. In other examples, functional blocks may be combined, or functions may be combined with... Figure 3A The different groupings shown are illustrated. Other circuitry 113 may include power supply circuitry and other processing circuitry that can use the output of accelerometer 110 to perform various functions, such as inertial navigation and motion sensing.

[0061] System 100 may include processing circuitry 102, resonator drive circuits 104A and 104B, and accelerometer 110. Accelerometer 110 may include any VBA, including those described above relative to... Figures 1 to 4 The suspended test mass block VBA accelerometer is mentioned above.

[0062] exist Figure 3A In the example, 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 sensing signals 108A and 108B from accelerometer 110. Figure 3A In the example, the resonator drive circuit 104A can be coupled to a resonator (e.g., Figure 1 The resonator 104A is depicted in the diagram, and the resonator drive circuit 104B may be coupled to a second resonator (e.g., 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 frequencies of each resonator. In some examples, the vibrating device excites and sustains the mechanical motion of each resonator via 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 the support base of the accelerometer (such as the one described above relative to...). Figure 2The support base 36) may travel along a conductive path within the support base. Signals from the resonator drive circuits 104A and 104B can provide a patterned electric field such that the resonator of the accelerometer 110 remains resonant. The processing circuit 102, combined with the resonator drive circuits 104A and 104B, may be as described above relative to... Figure 1 Examples of the control electronic devices described.

[0063] 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. Figure 3A Examples can be configured to determine differential frequency signals based on sensing signals 108A and 108B. Resonator drive circuits 104A and 104B can adjust the outputs of drive signals 106A and 106B based on feedback loops from sensing signals 108A and 108B, for example, to maintain the resonators at their respective resonant frequencies. As described above, a VBA according to this disclosure may include one or more resonators, and may also include fewer or additional resonator drive circuitry.

[0064] In this disclosure, a "differential frequency" measurement may include a combination of frequencies other than simple subtraction. In some examples, as part of a differential frequency measurement, the output of the first resonator may be weighted differently from the output of the second or third resonator. For example, as part of determining a differential frequency measurement, the first resonator may be weighted to 98% of the resonator output compared to the other resonators. In other examples, as part of determining a differential frequency measurement, the output of each resonator may be squared or otherwise processed. In other examples, any combination of weighting, square values, square roots, reciprocals, or other processing may be part of determining a differential frequency measurement.

[0065] As mentioned above, in contrast to Figure 1 and Figure 2 The acceleration of the suspended mass VBA, for example, in a direction substantially parallel to the plane of the test mass, can cause the suspended test mass to rotate about a hinge flexure parallel to the plane of the test mass. The resonator of the accelerometer 110 can be configured to receive a force in response to the rotation of the test mass, such that the force causes the resonator to bend in the plane of the test mass and results in a corresponding change in the resonant frequency of at least one resonator.

[0066] Processing circuitry 102 can communicate with resonator drive circuits 104A and 104B. Processing circuitry 102 may include various signal processing functions, such as filtering, amplification, and analog-to-digital conversion (ADC). Filtering functions may include high-pass, band-pass, or other types of signal filtering. In some examples, resonator drive circuits 104A and 104B may also include signal processing functions such as amplification and filtering. Processing circuitry 102 can output the processed signal received from accelerometer 110 as an analog or digital signal to other circuitry 113. Processing circuitry 102 can also receive signals from other circuitry 113, such as command signals, calibration signals, and similar signals.

[0067] Processing circuitry 102 may be operatively connected to accelerometer 110, for example, via resonator drive circuits 104A and 104B. Processing circuitry 102 may be configured to receive signals from accelerometer 110 that indicate a corresponding change in the resonant frequency of at least one resonator of accelerometer 110. Based on the corresponding change in resonant frequency, processing circuitry 102 may determine an acceleration measurement. In other examples (… Figure 3A In (not shown), the processing circuit 102 may be part of the 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.

[0068] Figure 3B This is a block diagram illustrating an accelerometer system 101 according to one or more technologies of this disclosure. Figure 3B As shown, the accelerometer system 101 includes a processing circuit 103, resonator drive circuits 105A-105B (collectively referred to as "resonator drive circuit 105"), and a test mass block assembly 111. The test mass block assembly 111 includes a test mass block 112, a resonator connection structure 116, a first resonator 120, and a second resonator 130. The first resonator 120 includes a first mechanical beam 124A and a second mechanical beam 124B (collectively referred to as "mechanical beam 124"), and a first set of electrodes 128A, a second set of electrodes 128B, and a third set of electrodes 128C (collectively referred to as "electrodes 128"). The second resonator 130 includes a third mechanical beam 134A and a fourth mechanical beam 134B (collectively referred to as "mechanical beam 134"), and a fourth set of electrodes 138A, a fifth set of electrodes 138B, and a sixth set of electrodes 138C (collectively referred to as "electrodes 138").

[0069] In some examples, the accelerometer system 101 may be configured to determine the relationship between the accelerometer and the object ( ) based on the measured vibration frequency of one or both of the first resonator 120 and the second resonator 130 connected to the test mass block 112. Figure 3B(Not shown in the image) The associated acceleration. In some cases, the vibrations of the first resonator 120 and the second resonator 130 are caused by drive signals emitted by the resonator drive circuit 105A and the resonator drive circuit 105B, respectively. Subsequently, the first resonator 120 may output a first set of sensing signals, and the second resonator 130 may output a second set of sensing signals, and the processing circuit 103 may determine the acceleration of the object based on the first set of sensing signals and the second set of sensing signals.

[0070] In some examples, processing circuitry 103 may include one or more processors configured to implement functions and / or processing instructions for execution within accelerometer system 101. For example, processing circuitry 103 may be capable of processing instructions stored in a storage device. Processing circuitry 103 may include, for example, a microprocessor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or equivalent discrete or integrated logic circuitry, or a combination of any of the foregoing devices or circuits. Therefore, processing circuitry 103 may include any suitable structure, whether in hardware, software, firmware, or any combination thereof, to perform the functions described herein for processing circuitry 103.

[0071] Memory ( Figure 3B (Not shown) can 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 disk, optical disk, flash memory, or electrically programmable memory (EPROM) or electrically erasable programmable memory (EEPROM). In some examples, the memory is used to store program instructions executed by the processing circuitry 103.

[0072] In some examples, the resonator drive circuit 105A may be electrically coupled to the first resonator 120. The resonator drive circuit 105A may output a first set of drive signals to the first resonator 120, causing the first resonator 120 to oscillate at its resonant frequency. Additionally, in some examples, the resonator drive circuit 105A may receive a first set of sense signals from the first resonator 120, wherein the first set of sense signals may indicate the mechanical vibration frequency of the first resonator 120. The resonator drive circuit 105A may output the first set of sense signals to the processing circuit 103 for analysis. In some examples, the first set of sense signals may represent a data stream, allowing the processing circuit 103 to determine the mechanical vibration frequency of the first resonator 120 in real-time or near real-time.

[0073] In some examples, the resonator drive circuit 105B may be electrically coupled to the second resonator 130. The resonator drive circuit 105B may output a second set of drive signals to the second resonator 130, causing the second resonator 130 to oscillate at its resonant frequency. Additionally, in some examples, the resonator drive circuit 105B may receive a second set of sensing signals from the second resonator 130, wherein the second set of sensing signals may indicate the mechanical vibration frequency of the first resonator 130. The resonator drive circuit 105B may output the second set of sensing signals to the processing circuit 103 for analysis. In some examples, the second set of sensing signals may represent a data stream, allowing the processing circuit 103 to determine the mechanical vibration frequency of the second resonator 130 in real-time or near real-time.

[0074] The test mass assembly 111 can use a first resonator 120 and a second resonator 130 to secure the test mass 112 to the resonator connection structure 116. For example, the test mass 112 can be secured to the resonator connection structure 116 in a first direction using a hinge flexure 114. The test mass 112 can be secured to the resonator connection structure 116 in a second direction using the first resonator 120 and the resonator 130. The test mass 112 can be configured to pivot about the hinge flexure 114, thereby applying pressure to the first resonator 120 and the second resonator 130 in the second direction. For example, if the test mass 112 pivots toward the first resonator 120, the test mass 112 applies a compressive force to the first resonator 120 and a tensile force to the second resonator 130. If the test mass 112 pivots toward the second resonator 130, the test mass 112 applies a tensile force to the first resonator 120 and a compressive force to the second resonator 130.

[0075] The acceleration of the test mass assembly 111 can affect the degree to which the test mass 112 pivots about the hinge flexure 114. Thus, 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 the acceleration of the test mass assembly 111. The amount of force (e.g., compressive or tensile force) applied to the resonators 120 and 130 can be correlated with the acceleration vector of the test mass assembly 111, which is perpendicular to the hinge flexure 114.

[0076] In some examples, the magnitude of the force applied to the first resonator 120 may be related to the resonant frequency at which the first resonator 120 vibrates in response to the resonator drive circuit 105A outputting a first set of drive signals to the first resonator 120. For example, the first resonator 120 may include mechanical beams 124. Thus, the first resonator 120 may represent a double-ended tuning fork (DETF) structure, wherein each mechanical beam in the mechanical beams 124 vibrates at a resonant frequency in response to receiving the first set of drive signals. Electrodes 128 may generate electrical signals indicating the mechanical vibration frequencies of the first mechanical beam 124A and the second mechanical beam 124B. For example, the first set of electrodes 128A may generate a first electrical signal, the second set of electrodes 128B may generate a second electrical signal, and the third set of electrodes 128C may generate a third electrical signal. Electrodes 128 may output the first, second, and third electrical signals to the processing circuit 103.

[0077] Processing circuit 103 can determine the difference between a first electrical signal and a second electrical signal, and determine the mechanical vibration frequency of the first mechanical beam 124A based on the difference between the first and second electrical signals. Additionally or alternatively, processing circuit 103 can determine the difference between a second electrical signal and a third electrical signal, and determine the mechanical vibration frequency of the second mechanical beam 124B based on the difference between the second and third electrical signals. In some examples, when resonator drive circuit 105A outputs a first set of drive signals to the first resonator 120, the mechanical vibration frequencies of the first mechanical beam 124A and the second mechanical beam 124B are substantially the same. For example, the mechanical vibration frequencies of the first mechanical beam 124A and the second mechanical beam 124B can both represent the resonant frequency of the first resonator 120, which is related to the magnitude of the force applied to the first resonator 120 by the test mass block 112. The magnitude of the force applied by the test mass 112 to the first resonator 120 can be related to the acceleration of the test mass assembly 111 relative to the long axis of the resonator connection structure 116. Thus, the processing circuit 103 can calculate the acceleration of the test mass 112 relative to the long axis of the resonator connection structure 116 based on the detected mechanical vibration frequency of the mechanical beam 124.

[0078] In some examples, the magnitude of the force applied to the second resonator 130 may be related to the resonant frequency at which the second resonator 130 vibrates in response to the second set of drive signals output to the second resonator 130 by the resonator drive circuit 105B. For example, the second resonator 130 may include mechanical beams 134. Thus, the second resonator 130 may represent a double-ended tuning fork (DETF) structure, wherein each mechanical beam of the mechanical beams 134 vibrates at a resonant frequency in response to receiving the second set of drive signals. Electrodes 138 may generate electrical signals indicating the mechanical vibration frequencies of the third mechanical beam 134A and 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. Electrodes 138 may output the fourth, fifth, and sixth electrical signals to the processing circuit 103.

[0079] Processing circuit 103 can determine the difference between the fourth and fifth electrical signals, and determine the mechanical vibration frequency of the third mechanical beam 134A based on the difference between the fourth and fifth electrical signals. Additionally or alternatively, processing circuit 103 can determine the difference between the fifth and sixth electrical signals, and determine the mechanical vibration frequency of the fourth mechanical beam 134B based on the difference between the fifth and sixth electrical signals. In some examples, when resonator drive circuit 105B outputs the second set of drive signals to the second resonator 130, the mechanical vibration frequencies of the third mechanical beam 134A and the fourth mechanical beam 134B are substantially the same. For example, the mechanical vibration frequencies of the third mechanical beam 134A and the fourth mechanical beam 134B can both represent the resonant frequency of the second resonator 130, which is related to the magnitude of the force applied to the second resonator 130 by the test mass block 112. The magnitude of the force applied by the test mass 112 to the second resonator 130 can be related to the acceleration of the test mass assembly 111 relative to the long axis of the resonator connection structure 116. Thus, the processing circuit 103 can calculate the acceleration of the test mass 112 relative to the long axis of the resonator connection structure 116 based on the detected mechanical vibration frequency of the mechanical beam 134.

[0080] In some cases, the processing circuit 103 can calculate the acceleration of the test mass assembly 111 relative to the long axis of the resonator connection structure 116 based on the difference between the detected mechanical vibration frequency of the mechanical beam 124 and the detected mechanical vibration frequency of the mechanical beam 134. When the test mass assembly 111 accelerates in a first direction along the long axis of the resonator connection structure 116, the test mass 112 pivots toward the first resonator 120, such that the test mass 112 applies a compressive force to the first resonator 120 and a tensile force to the second resonator 130. When the test mass assembly 111 accelerates in a second direction along the long axis of the resonator connection structure 116, the test mass 112 pivots toward the second resonator 130, such that the test mass 112 applies a tensile force to the first resonator 120 and a compressive force to the second resonator 130. When the first compressive force is less than the second compressive force, the resonant frequency of the resonator with the first compressive force applied can be greater than the resonant frequency of the resonator with the second compressive force applied. When the first tension is greater than the second tension, the resonant frequency of the resonator with the first tension applied can be greater than the resonant frequency of the resonator with the second tension applied.

[0081] Although the accelerometer system 101 is shown as including the resonator connection structure 116, in Figure 3B In some examples not shown, the test mass 112, the first resonator 120, and the second resonator 130 are not connected to the resonator connection structure. In some such examples, the test mass 112, the first resonator 120, and the second resonator 130 are connected to the substrate. For example, a hinge flexure 114 can fix the test mass 112 to the substrate such that the test mass 112 can pivot about the hinge flexure 114, thereby applying tension and / or compressive forces to the first resonator 120 and the second resonator 130.

[0082] In some examples, the difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130 may have an approximately linear relationship with the acceleration of the test mass assembly 111. In some examples, the relationship between the difference in the resonant frequencies of the resonators 120 and 130 and the acceleration of the test mass assembly 111 may not be perfectly linear. For example, the relationship may include a quadratic nonlinear coefficient (K2) representing a nonlinear relationship between the difference in the resonant frequencies of the resonators 120 and 130 and the acceleration of the test mass assembly 111. It may be advantageous for the quadratic nonlinear coefficient to be zero or close to zero, such that the processing circuit 103 is configured to accurately determine the acceleration of the test mass assembly 111 based on the relationship between the difference in the resonant frequencies of the resonators 120 and 130 and the acceleration of the test mass assembly 111. One type of error is vibration rectification error (VRE). VRE can be a change in zero-gravity output or accelerometer bias that occurs during vibration. VRE can be caused by nonlinearity in the accelerometer input-to-output transfer function. Typically, the primary source is the quadratic nonlinearity coefficient (K2). To avoid VRE, mitigating this quadratic nonlinearity may be beneficial.

[0083] Additionally, it may be advantageous when the acceleration of the test mass block assembly 111 is zero m / s². 2 At that time, the difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130 is not zero. Compared to a system where the difference between the corresponding resonant frequencies of the first and second resonators at zero acceleration is zero or closer to zero than the system described herein, it may be advantageous that the difference between the corresponding resonant frequencies of resonators 120 and 130 is not zero when the test mass assembly 111 is not accelerating, in order to reduce interference between the first resonator 120 and the second resonator 130.

[0084] In some examples, the accelerometer system 101 ensures that the second-order nonlinear coefficient is close to zero, and ensures that the zero-acceleration difference at the respective resonant frequencies of resonators 120 and 130 is not zero by including additional mass blocks 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 mass blocks, wherein the one or more additional mass blocks 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, with additional mass blocks 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 additional mass blocks on the first mechanical beam 124A and the second mechanical beam 124B, while the third mechanical beam 134A includes gaps corresponding to the additional mass blocks on the first mechanical beam 124A, and the fourth mechanical beam 134B includes gaps corresponding to the additional mass blocks on the second mechanical beam 124B. Such a difference between the first resonator 120 and the second resonator 130 ensures that the second-order nonlinear coefficient is close to zero (e.g., less than 5 μg / g). 2 And ensure that the zero acceleration difference of the corresponding resonant frequencies of resonators 120 and 130 is not zero.

[0085] For a VBA with two identical resonators, even-order nonlinearities (e.g., second-order or fourth-order nonlinearities) are common-mode error sources nominally eliminated through differential output. However, mismatched resonators (such as the first resonator 120 and the second resonator 130) may cause the accelerometer's K2 to not necessarily be set to zero. Mismatched resonators may be necessary to avoid operating the two resonators at the same frequency. Driving two resonators at similar frequencies can cause them to interfere with each other (mechanical and electrical interference), which ultimately degrades the VBA's output. Resonators 120 and 130 ensure that K2 is zero or close to zero and reduce such interference that degrades the VBA's output.

[0086] Although the accelerometer system 101 is described as having two resonators, Figure 3B In other examples not shown, the accelerometer system may include fewer than two resonators or more than two resonators. For example, one accelerometer system may include one resonator. Another accelerometer system may include four resonators.

[0087] Figure 4 This is a conceptual diagram illustrating an example of resonator electrode placement and electrical signal routing to avoid the effects of parasitic feedthrough capacitance on accelerometer performance. The VBA 830 is the above-mentioned... Figure 1 , Figure 2Examples of VBA 30, VBA 50, and VBA430 as shown in Figure 4. The suspension test mass block 832, resonator 818, resonator beam 819, flexure 833, and mechanical anchor 814 are, in relation to the above, examples of VBA 30, VBA 50, and VBA430. Figure 1 and Figure 4 Examples of the inspection mass block 32, resonators 18A and 18B, resonator beams 19A and 19B, flexure 33 and mechanical anchor 14 described above, and therefore may have the same description, characteristics and functions as described above. Figure 4 Examples of VBA 830 include a damping comb 840. However, in other examples, the VBA 830 may not have a damping comb 840.

[0088] The electrodes and routing within both the electronic components and the VBA mechanism can generate a certain parasitic capacitance between the drive electrode and the sensing electrode. An example of a VBA 830 includes resonator electrodes, such as drive electrodes 838 and 839, configured to mitigate the effects of the parasitic capacitance inherent in the VBA resonator. Thus, if the feedthrough capacitance between each drive electrode and the sensing electrode is similar, the feedthrough currents will be out of phase with each other, resulting in zero net current.

[0089] Control electronics can be connected to the resonator drive electrodes (such as drive electrodes 838 and 839) to maintain the movement of the vibrating beam 819. The electrodes and routing within both the electronics and the VBA mechanism can generate some parasitic capacitance between the drive electrodes and the sensing electrodes. Figure 4 In the example, two different drive electrodes 838 and 839 can receive voltage signals of opposite polarity. Drive electrodes 838 and 839 can be located on opposite sides of a moving MEMS element (e.g., resonator 818), allowing an actuator to push and pull to drive resonator 818. In some examples, the inverted drive signals can be generated by analog electronics within the control electronics of the VBA. Thus, if the feedthrough capacitance between each drive electrode and the sensing electrode is similar, the feedthrough currents will be out of phase, resulting in zero net current.

[0090] In some alternative examples, such as configurations with a single drive and sensing electrode, the parasitic feedthrough capacitance can result in a feedthrough current between the drive and sensing electrodes. This feedthrough current can be added to the motional current caused by the movement of the mechanical resonator. This total output current is read by the front-end electronics and ultimately used to sustain and sense the frequency of the mechanical oscillation. Therefore, the feedthrough current caused by the feedthrough capacitance can affect the resonator transfer function and the operation of the VBA.

[0091] For moderate feedthrough capacitance, the magnitude and phase of the resonator transfer function can degrade, potentially leading to increased accelerometer noise. If the resonator is driven too far from mechanical resonance, the stability of the accelerometer bias can degrade because the resonator frequency will be more susceptible to any phase shift in the electronics. Therefore, avoiding the effects of this parasitic feedthrough capacitance can ultimately improve accelerometer performance.

[0092] The techniques disclosed herein may include configuring the capacitive comb fingers of resonator 818 as discrete electrodes including drive electrodes 838 and 839 and two sensing electrodes (sensing-856 and sensing+858). The sensing electrodes (i.e., sensing-856 and sensing+858) may be coupled to an anchored 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 substantially equal parasitic feedthrough capacitances Cf+ and Cf-. In some examples, one or more of the electrical signals may include an additional routing 824 to ensure that the parasitic feedthrough capacitances Cf+ and Cf- are substantially equal. Electrical signals 850, 852, and 854 may be connected to terminals such as drive 820, sensing-802, and sensing+810, respectively.

[0093] The two sensing electrodes on the VBA can be placed on opposite sides of the moving MEMS resonator beam 819 such that the magnitudes of the capacitance change (dCs / dx) relative to the displacement are approximately equal and opposite in sign. Then, the sensing current (i... s+ and i s- The sign of the feedthrough current (i) will be reversed, but the sign of the feedthrough current (i) will be reversed. f+ and i f- The sense outputs 802 and 810 will have the same sign. These can be connected to a differential front-end amplifier (such as a transimpedance or charge amplifier) ​​that handles the differences in the output current. In this way, the feedthrough currents roughly cancel each other out and the effects are mitigated.

[0094] Alternative solutions may exist to avoid feedthrough capacitance effects, but these involve additional electronic complexity that can increase cost. Some exemplary alternatives may include using a sinusoidal voltage at half the mechanical resonant frequency to drive the resonator. Since electrostatic force is proportional to the square of the voltage, an electrostatic actuator could potentially generate force at twice the frequency of the sinusoidal voltage. This alternative solution could eliminate the possibility of feedthrough to the sensing capacitor if the drive signal has a low second harmonic content, since the drive and sensing signals have different frequencies. However, this alternative solution would likely require the use of a microcontroller within the resonator feedback loop. Adding a digital microcontroller could result in an accelerometer that is significantly larger and more expensive than one with an analog control loop.

[0095] Another alternative example uses two different sensing electrodes biased by voltages of opposite polarities. The resulting output current can then be differentially divided to eliminate the effects of feedthrough capacitance. However, sensing electrodes with opposite polarities may have the disadvantage of requiring two large bias voltages instead of just one.

[0096] A third alternative uses two different drive electrodes that receive inverted voltage signals. If the feedthrough capacitance between each drive electrode and the sensing electrode is similar, the feedthrough currents will be out of phase, resulting in 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 can be generated by analog electronics and may have the disadvantage of requiring two separate drive circuits.

[0097] Measurement results of the resonator configuration techniques disclosed herein demonstrate improvements in the open-loop phase response of analog electronics, which are expected to improve noise and, in some examples, bias stability. These techniques can be unique compared to other exemplary techniques because, in some examples, the VBA typically uses one drive electrode and one sensing electrode per resonator. Given a drive and one sensing configuration, there is no means to eliminate any feedthrough capacitance that may occur. Instead, other examples may simply attempt to minimize this capacitance.

[0098] The technical benefits of this disclosure include eliminating or reducing the effects of the drive-to-sensor feedthrough capacitance. Reduced capacitance improves the open-loop phase response of the resonator-integrated electronics, which in turn allows the electronics to directly drive the resonator under mechanical resonance. In some examples, these techniques make accelerometer devices easier to integrate with small changes in the electronics, ultimately relaxing the requirements on the electronics themselves. Additionally, prior to the development of readout electronics, there may be a concern that this feedthrough capacitance will negatively impact the performance of the electronics. The readout circuit is a circuit that can be configured to convert information about capacitance changes caused by external acceleration into a voltage signal. Test measurements show that eliminating these feedthrough currents leads to an improvement in the open-loop response of the resonator.

[0099] The techniques disclosed herein for eliminating feedthrough current can be incorporated into MEMS VBA. Each resonator 818 may have an electrode wired to its corresponding bonding pad. The input to each resonator 818 may be a single drive voltage, while the output may be configured as two sensing electrodes 841 and 842, which contain nominal out-of-phase currents representing the physical motion of the MEMS resonator.

[0100] In the example of a double-ended tuning fork resonator, each resonator has two moving parts that oscillate in opposite directions. Drive electrodes (e.g., drive electrodes 838 and 839) can supply a drive voltage that excites mechanical motion at resonance. VBA 830 may include... Figure 4 Additional drive electrodes are not shown. When the two resonator tips move away from each other, the positive sensing electrode (e.g., 858) can generate a positive current. When the two resonator tips move together, the negative sensing electrode (e.g., 856) can generate a positive current. Therefore, the sensing electrodes are oriented to have similar magnitudes but opposite signs of dC / dx. The routing of electrical signals 850, 852, and 854 on the MEMS die can be configured to have similar feedthrough capacitances between the drive electrodes and the sensing electrodes.

[0101] Figure 5A and Figure 5B This is a schematic diagram illustrating an exemplary MEMS VBA configured with a single sensing electrode. Figure 5A A mechanical model of an exemplary single sensing electrode VBA is shown, and Figure 5B The equivalent circuit is shown.

[0102] exist Figure 5A In the example, the DC bias voltage Vb 902 is connected to the MEMS electrode at mass block 910, where mass block 910 represents the mass block of the resonator beam, not the test mass block of the VBA. Mass block 910 is connected to attachment point 922 via spring 916 with spring constant K, to attachment point 923 via variable drive capacitor Cd 912, and to attachment point 924 via variable sensing capacitor Cs 914. As described above, relative to, for example... Figure 1 The capacitance can change when the resonator tip for the release region moves relative to the resonator tip for the anchoring region.

[0103] An AC drive voltage Vd 904 is connected to the drive electrode at attachment point 923 to excite mechanical motion in the resonator and cause the mass block 910 to move along the X-axis 918. (As described above...) Figure 4 The electrode location and signal routing can create a parasitic capacitance, such as a feedthrough capacitance Cf 908, between the drive electrode and the sensing electrode. In an exemplary configuration of the resonator 900 with a single drive and sensing electrode, this parasitic feedthrough capacitance Cf 908 can result in a feedthrough current between the drive electrode and the sensing electrode, which can be received by an amplifier connected to the VBA.

[0104] Figure 5B Circuit 950 in the example is Figure 5AThe equivalent circuit of resonator 900 described herein. The mass block and other components of resonator 900 can be modeled as an RLC circuit of MEMS 952. MEMS 952 includes resistor R 932 connected in series with inductor L 930 and capacitor C934. The first terminal of resistor R 932 is connected to the AC drive voltage Vd 904. The second terminal of resistor R 932 is connected to the first terminal of inductor L 930. The second terminal of inductor L 930 is connected to the first terminal of capacitor C934. The second terminal of capacitor C 934 is connected to node 942, which also includes connections to feedthrough capacitor Cf 908, resistor R 935, and capacitor Cblock 940. Another terminal of Cblock 940 is connected to a terminal that can output the sensed signal to an amplifier. Bias voltage Vb 902 is connected to the same node 942 via resistor R 935.

[0105] The dynamic current or sensed current i caused by the AC drive voltage 904 m 958 moves through MEMS 952. The geometry of the electrodes and conductors can lead to unwanted feedthrough currents. f 956. Feed current i f 956 is added at node 942 to the motional current i induced by the movement of the mechanical resonator. m 958, and as i m +i f (954) Output to amplifier. This total output current can be read by the front-end electronics. The total current can degrade the resonator transfer function, which can lead to increased accelerometer noise. If the resonator is driven away from mechanical resonance, the additional feedthrough current can degrade the stability of the accelerometer bias.

[0106] Figure 6A and Figure 6B This is a schematic diagram illustrating an exemplary MEMS VBA configured with two sensing electrodes. Figure 6A A mechanical model of an exemplary single sensing electrode VBA is shown, and Figure 6B The equivalent circuit is shown. The arrangement of resonator 1000 and circuit 1050 eliminates at least some of the unwanted feed current and reduces the effect of feed capacitance.

[0107] exist Figure 6A In the example, mass 1010 is connected to attachment point 1022 via spring 1016 having a spring constant K and to attachment point 1023 via variable drive capacitor Cd 1012. For the sensing electrode, mass 1010 is connected to attachment point 1024 via variable sensing capacitor Cs- 1015 and to attachment point 1025 via variable sensing capacitor Cs+ 1014.

[0108] An AC drive voltage Vd 1004 is connected to the drive electrode at attachment point 1023 to excite mechanical motion in the resonator and cause the mass block 1010 to move along the X-axis 1018. (As described above, relative to...) Figure 4 The electrode positions and signal routing can generate parasitic capacitance between the driving electrode and the sensing electrode. In the example of resonator 1000, the positive feedthrough capacitance Cf+1008 can be caused by the parasitic capacitance between the driving circuit, including Cs+1014, and the sensing circuit. The negative feedthrough capacitance Cf-1018 can be caused by the parasitic capacitance between the driving circuit, including Cs-1015, and the sensing circuit.

[0109] As mentioned above, in contrast to Figure 4 As the resonator teeth move away, the positive sensing electrode of the resonator (denoted by Cs+1014) generates a positive current. When the resonator teeth move together, the negative sensing electrode (denoted by Cs-1015) generates a positive current. Therefore, the sensing electrodes are oriented to have similar magnitudes but opposite signs of dC / dx. The routing of electrical signals 850, 852, and 854 on the MEMS die can be configured to have similar feedthrough capacitances between the drive electrode and the positive and negative sensing electrodes, such that Cf+1008 and Cf-1018 are approximately equal. In this disclosure, approximately equal means equal within manufacturing and measurement tolerances. Small variations in materials, processes, etc., during manufacturing can lead to small differences, such that, for example, CF-1018 and CF+1008 may be approximately equal rather than exactly equal. The sensing output from resonator 1000 can be processed by differential amplifier 1020 so that the positive feedthrough current and the negative feedthrough current can be largely canceled out of each other.

[0110] exist Figure 6B In the example, circuit 1050 is Figure 6AThe equivalent circuit of resonator 1000 described in [the diagram] is shown. The mass block and other components of resonator 900 can be modeled as two RLC circuits of MEMS 1052. For the positive sensing branch, MEMS 1052 includes a resistor R 1032 connected in series with inductor L 1030 and capacitor C 1034. The first terminal of resistor R 1032 is connected to the AC drive voltage +Vd 1040. The second terminal of resistor R 1032 is connected to the first terminal of inductor L 1030. The second terminal of inductor L 1030 is connected to the first terminal of capacitor C 1034. The second terminal of capacitor C 1034 is connected to output node 1042, which also includes a connection with feedthrough capacitor Cf+ 1008. AC drive voltage +Vd 1040 and AC drive voltage -Vd 1041 indicate that the drive voltages are out of phase. Although depicted as two separate AC sources in the example of circuit 1050, in other examples, a single AC source can provide the drive signal, and the analog circuit can, for example, output an AC drive signal with opposite phase. For example, the above combined... Figure 3A and Figure 3B The resonator drive circuits 103A, 103B, 104A and 104B may include an AC drive circuit configured to provide drive signals with opposite phase to the resonator.

[0111] For the negative sensing branch, MEMS 1052 includes a resistor R 1033 connected in series with inductor L 1031 and capacitor C 1035. The first terminal of resistor R 1033 is connected to the AC drive voltage -Vd 1041. The second terminal of resistor R 1033 is connected to the first terminal of inductor L 1031. The second terminal of inductor L 1031 is connected to the first terminal of capacitor C 1035. The second terminal of capacitor C 1035 is connected to output node 1043, which also includes a connection to feedthrough capacitor Cf-1018.

[0112] The motional current caused by AC drive voltages 1040 and 1041 shifts through the positive branch of MEMS 1052 (which includes R1032, e.g., i...). m+ 1058) and through the negative branch (which includes R 1033, e.g. i m- 1059) Both. Electrode and conductor geometries can lead to unwanted feed currents i f+ 1056 and i f- 1057. On the positive side, the feed current i f+ 1056 is added to the motional current i caused by the motion of the mechanical resonator. m+ 1058, and as i m+ +i f+The 1054 output is fed to one input of the differential amplifier 1020. On the negative side, the feedthrough current i f- 1057 added to motional current i m- 1059 and as i m- +i f+ The output of the 1055 is fed to the second input of the differential amplifier 1020. In formulaic form, the result can be described as:

[0113] • The positive sensing current and the negative sensing current are approximately equal: i m+ =-i m-

[0114] • The positive feedthrough capacitance and the negative feedthrough capacitance are approximately equal:

[0115]

[0116] Therefore, the output of the differential amplifier is:

[0117] i diff =i m+ +i f+ -(i f- +i m- )=2*i m+

[0118] Figure 7A This is a conceptual diagram illustrating a first resonator 1120 with an additional mass block according to one or more techniques of this disclosure. The first resonator 1120 can be... Figure 1 The resonator 18 and Figure 3B An example of a first resonator 120. The first resonator 1120 may include anchoring combs 1122A-1122C (collectively referred to as "anchoring comb 1122"), a first mechanical beam 1124A, and a second mechanical beam 1124 (collectively referred to as "mechanical beam 1124"). The first mechanical beam 1124A may include additional mass blocks 1162A-1162D (collectively referred to as "additional mass blocks 1162"). The second mechanical beam 1124B may include additional mass blocks 1164A-1164D (collectively referred to as "additional mass blocks 1164").

[0119] 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 a combination of the anchoring comb portions of anchoring comb 1122A may include a first set of electrodes (e.g., Figure 3BThe first set of electrodes 128A may contain one or more electrodes. In some examples, any or a combination of the anchoring comb portions of the anchoring comb 1122B may include one or more electrodes from the second set of electrodes (e.g., the second set of electrodes 128A). In some examples, any or a combination of the anchoring comb portions of the anchoring comb 1122C may include one or more electrodes from the third set of electrodes (e.g., the third set of electrodes 128C).

[0120] In some examples, the resonator drive circuit can transmit a drive signal to the first resonator 1120 via any one or a combination of the first set of electrodes, the second set of electrodes, and the third set of electrodes, causing the first resonator 1120 to oscillate at its resonant frequency. For example, the first mechanical beam 1124A and the second mechanical beam 1124B can oscillate at the aforementioned resonant frequency. Subsequently, the first set of electrodes can generate a first electrical signal, the second set of electrodes can generate a second electrical signal, and the third set of electrodes can generate a third electrical signal. The first resonator 1120 can output the first, second, and third electrical signals to a processing circuit. Figure 7A (Not shown in the image), the processing circuit is configured to determine the resonant frequency of the first resonator 1120 based on the first electrical signal, the second electrical signal, and the third electrical signal.

[0121] In some examples, the resonant frequency of the first resonator 1120 can be related to that of the test mass block (such as...). Figure 1 Inspection quality block 32 and Figure 3B The magnitude of the force applied to the first resonator 1120 by the test mass block 112 is related to the strength of the force. For example, the first end 1182 of the first resonator 1120 can be fixed to a resonator connection structure (e.g., Figure 1 The resonator connection structure 16 and Figure 3B The resonator connection structure 116 is provided, and the second end 1184 of the first resonator 1120 can be fixed to the test mass block. If the test mass block rotates toward the first resonator 1120 in response to acceleration in a first direction, the test mass block can apply a compressive force to the first resonator 1120. If the test mass block rotates away from the first resonator 1120 in response to acceleration in a second direction, the test mass block can apply a tensile force to the first resonator 1120. In some examples, if the acceleration is zero m / s², 2 If the test mass block does not apply force to the first resonator 1120, the resonant frequency of the first resonator 1120 may decrease as the compressive force applied by the test mass block increases in response to an increase in acceleration in the first direction, and the resonant frequency of the first resonator 1120 may increase as the tension applied by the test mass block increases in response to an increase in acceleration in the second direction. Thus, a relationship may exist between the resonant frequency of the first resonator 1120 and the acceleration of the accelerometer including the first resonator 1120.

[0122] The additional mass blocks 1162 and 1164 can influence the relationship between acceleration and the resonant frequency of the first resonator 1120. For example, the quadratic nonlinear coefficient defining the relationship between acceleration and the resonant frequency of the resonator excluding the additional mass blocks 1162 and 1164 may be smaller than the quadratic nonlinear coefficient defining the relationship between acceleration and the resonant frequency of the resonator excluding the additional mass blocks 1162 and 1164. It may be advantageous to make the relationship between acceleration and the resonant frequency of the first resonator 1120 as close to linear as possible (e.g., with a quadratic nonlinear coefficient as small as possible) to ensure that the electrical signal generated by the first resonator 1120 allows the processing circuitry to accurately determine the acceleration.

[0123] In some examples, additional mass blocks 1162A and 1162B may be positioned at a location along the first mechanical beam 1124A, within a range of 25% to 45% of the length along the first mechanical beam 1124A from the first end 1156 to the second end 1157. For example, additional mass blocks 1162A and 1162B may be positioned at a location at 35% of the distance between the first end 1156 and the second end 1157. In some examples, additional mass blocks 1162C and 1162D may be positioned at a location along the first mechanical beam 1124A, within a range of 55% to 75% of the length along the first mechanical beam 1124A from the first end 1156 to the second end 1157. For example, additional mass blocks 1162C and 1162D may be positioned at a location at 65% of the distance between the first end 1156 and the second end 1157.

[0124] In some examples, additional mass blocks 1164A and 1164B may be positioned at a location along the second mechanical beam 1124B, within a range of 25% to 45% of the length along the second mechanical beam 1124B from the first end 1158 to the second end 1159. For example, additional mass blocks 1164A and 1164B may be positioned at a location at 35% of the distance between the first end 1158 and the second end 1159. In some examples, additional mass blocks 1164C and 1164D may be positioned at a location along the second mechanical beam 1124B, within a range of 55% to 75% of the length along the second mechanical beam 1124B from the first end 1158 to the second end 1159. For example, additional mass blocks 1164C and 1164D may be positioned at a location at 65% of the distance between the first end 1158 and the second end 1159.

[0125] Figure 7BThis illustrates an embodiment of one or more technologies according to this disclosure, including additional mass blocks 1162A and 1162B. Figure 7A A conceptual diagram of a portion of the first resonator 1120. For example, the first mechanical beam 1124A includes a primary component 1190 and a set of secondary components 1192A-1192D (collectively referred to as the "set of secondary components 1192"). Figure 7B As shown, each of the secondary members in this group of secondary members 1192 extends perpendicular to the primary member 1190. The first mechanical beam 1124A may include Figure 7B Additional secondary components and other components not shown. Each secondary component in this group of secondary components 1192 may be substantially the same, except that secondary component 1192C includes additional mass block 1162A and additional mass block 1162B.

[0126] Figure 8A This is a conceptual diagram illustrating a second resonator 1230 forming a gap according to one or more techniques of this disclosure. The second resonator 1230 can be... Figure 3B An example of a second resonator 130. The second resonator 1230 may include anchoring combs 1232A-1232C (collectively referred to as "anchoring comb 1232"), a third mechanical beam 1234A, and a fourth mechanical beam 1234B (collectively referred to as "mechanical beam 1234"). The third mechanical beam 1234A may form gaps 1262A-1262D (collectively referred to as "gap 1262"). The fourth mechanical beam 1234B may form gaps 1264A-1264D (collectively referred to as "gap 1264").

[0127] In some examples, anchoring comb 1232A may include one or more anchoring comb portions, anchoring comb 1232B may include one or more anchoring comb portions, and the anchoring comb may include one or more anchoring comb portions. In some examples, any one or a combination of the anchoring comb portions of anchoring comb 1232A may include a fourth set of electrodes (e.g., Figure 3B The fourth group of electrodes 138A may include one or more electrodes. In some examples, any or a combination of the anchoring comb portions of the anchoring comb 1232B may include one or more electrodes of the fifth group of electrodes (e.g., the fifth group of electrodes 138B). In some examples, any or a combination of the anchoring comb portions of the anchoring comb 1232C may include one or more electrodes of the sixth group of electrodes (e.g., the sixth group of electrodes 138C).

[0128] In some examples, the resonator drive circuit can transmit a drive signal to the second resonator 1230 via any one or a combination of the fourth, fifth, and sixth sets of electrodes, causing the second resonator 1230 to oscillate at its resonant frequency. For example, the third mechanical beam 1234A and the fourth mechanical beam 1234B can oscillate at the resonant frequency of the second resonator 1230. Subsequently, the fourth set of electrodes can generate a fourth electrical signal, the fifth set of electrodes can generate a fifth electrical signal, and the sixth set of electrodes can generate a sixth electrical signal. The second resonator 1230 can output the fourth, fifth, and sixth electrical signals to a processing circuit. Figure 8A (Not shown in the image), the processing circuit is configured to determine the resonant frequency of the second resonator 1230 based on the fourth, fifth, and sixth electrical signals.

[0129] In some examples, the resonant frequency of the second resonator 1230 can be related to that of the test mass block (such as...). Figure 3B The magnitude of the force applied to the second resonator 1230 by the test mass block 112 is related to the magnitude of the force. For example, the first end 1282 of the second resonator 1230 may be fixed to the test mass block, and the second end 1284 of the second resonator 1230 may be fixed to the resonator connection structure (e.g., Figure 3B (Resonator connection structure 116). If the test mass rotates away from the second resonator 1230 in response to acceleration in the first direction, the test mass can apply tension to the second resonator 1230. If the test mass rotates towards the second resonator 1230 in response to acceleration in the second direction, the test mass can apply compressive force to the second resonator 1230. In some examples, if the acceleration is zero m / s²... 2 If the test mass block does not apply force to the second resonator 1230, the resonant frequency of the second resonator 1230 may decrease as the compressive force applied by the test mass block increases in response to an increase in acceleration in the second direction, and the resonant frequency of the second resonator 1230 may increase as the tension applied by the test mass block increases in response to an increase in acceleration in the first direction. Thus, a relationship may exist between the resonant frequency of the second resonator 1230 and the acceleration of the accelerometer including the second resonator 1230.

[0130] Gap 1262 and gap 1264 can affect the relationship between acceleration and the resonant frequency of the second resonator 1230. For example, the quadratic nonlinear coefficient defining the relationship between acceleration and the resonant frequency of the resonator excluding gaps 1262 and 1264 may be smaller than the quadratic nonlinear coefficient defining the relationship between acceleration and the resonant frequency of the resonator excluding gaps 1262 and 1264. It may be advantageous to make the relationship between acceleration and the resonant frequency of the second resonator 1230 as close to linear as possible (e.g., with the quadratic nonlinear coefficient as small as possible) to ensure that the electrical signal generated by the second resonator 1230 allows the processing circuitry to accurately determine the acceleration. In some examples, gap 1262 represents a "hole," while the additional mass block 1162 is included... Figures 7A to 7B On the first resonator 1120. In some examples, gap 1264 represents a hole, while additional mass block 1164 is included. Figures 7A to 7B On the first resonator 1120. The gap or hole of the additional mass block on the resonator is different from the hole in the test mass block configured to tune the mechanical mode, as described above relative to... Figure 4 As stated above.

[0131] In some examples, gaps 1262A and 1262B may be positioned at a location along the third mechanical beam 1234A, within a range of 25% to 45% of the length along the third mechanical beam 1234A from the first end 1256 to the second end 1257. For example, gaps 1262A and 1262B may be positioned at a location at 35% of the distance between the first end 1256 and the second end 1257. In some examples, gaps 1262C and 1262D may be positioned at a location along the third mechanical beam 1234A, within a range of 55% to 75% of the length along the third mechanical beam 1234A from the first end 1256 to the second end 1257. For example, gaps 1262C and 1262D may be positioned at a location at 65% of the distance between the first end 1256 and the second end 1257.

[0132] In some examples, gaps 1264A and 1264B may be positioned at a location along the fourth mechanical beam 1234B, within a range of 25% to 45% of the length along the fourth mechanical beam 1234B from the first end 1258 to the second end 1259. For example, gaps 1264A and 1264B may be positioned at a location at 35% of the distance between the first end 1258 and the second end 1259. In some examples, gaps 1264C and 1264D may be positioned at a location along the fourth mechanical beam 1234B, within a range of 55% to 75% of the length along the fourth mechanical beam 1234B from the first end 1258 to the second end 1259. For example, gaps 1264C and 1264D may be positioned at a location at 65% of the distance between the first end 1258 and the second end 1259.

[0133] Figure 8B This illustrates one or more technologies according to the present disclosure, including gaps 1262A and 1262B. Figure 8A A conceptual diagram of a portion of the second resonator 1230. For example, the third mechanical beam 1234A includes a primary component 1290 and a set of secondary components 1292A-1292D (collectively referred to as the "set of secondary components 1292"). Figure 8B As shown, each of the secondary members in this group of secondary members 1292 extends perpendicular to the primary member 1290. The third mechanical beam 1234A may include Figure 8B Additional secondary components and other components not shown. Each secondary component in this group of secondary components 1292 may be substantially the same, except that the distance between secondary component 1292C and secondary component 1292D is greater than the distance between any other pair of consecutive secondary components in this group of secondary components 1292.

[0134] Figure 9 This is a graph illustrating a first graph 1310 and a second graph 1320 according to one or more techniques of this disclosure. The first graph represents a quadratic nonlinear coefficient as a function of the position of the additional mass, and the second graph represents the zero-acceleration resonant frequency difference as a function of the position of the additional mass. For example, as... Figure 7AThe “Location of Added Mass” described herein can represent the position of added mass blocks such as added mass blocks 1162A and 1162B on the first mechanical beam 1124A, where the position is a percentage of the length from the first end 1156 to the second end 1157 of the first mechanical beam 1124A. As shown in the first curve 610 of Figure 6, when the positions of added mass blocks 1162A and 1162B are 35% of the length of the first mechanical beam 1124A, the quadratic nonlinear coefficient (K2) is zero. Furthermore, as seen at point 1330 of the second curve 1320, when the positions of added mass blocks 1162A and 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, since the second-order nonlinear coefficient is zero and the frequency difference is non-zero, it may be advantageous for the additional mass blocks 1162A and 1162B to be positioned at 35% of the length of the first mechanical beam 1124A.

[0135] In some examples, point 1330 may represent the ideal position of additional mass blocks 1162A and 1162B along the 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 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 kHz to 30 kHz. In some examples, when additional mass blocks 1162A and 1162B are placed at 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 Hz to 3500 Hz.

[0136] Figure 10 This is a flowchart illustrating exemplary operations for determining VBA acceleration according to one or more techniques of this disclosure. Figure 7 is about... Figure 3B The processing circuit 102, resonator drive circuit 104, and test mass block assembly 111 are described. However, the technique of FIG7 can be performed by different components of system 101, system 100 of FIG3A, or by an additional or alternative accelerometer system.

[0137] A resonator drive circuit 104A can transmit a set of drive signals to a first resonator 120 (1402). The resonator drive circuit 104A can be electrically coupled to the first resonator 120. The resonator drive circuit 104A can output the set of drive signals to the first resonator 120, causing the first resonator 120 to oscillate at its resonant frequency. A processing circuit 102 can receive one or more electrical signals (1404) indicating the frequencies of the first mechanical beam 124A and the second mechanical beam 124B via the resonator drive circuit 104A. Subsequently, the processing circuit 102 can determine the frequencies of the first mechanical beam 124A and the second mechanical beam 124B based on the aforementioned 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 can represent the resonant frequency of the first resonator 120. The resonant frequency of the first resonator 120 can be correlated with VBA (such as...). Figure 2 The acceleration of VBA 110 is related to the frequency of the first mechanical beam 124A and the second mechanical beam 124B. Thus, the processing circuit 102 can calculate the acceleration of VBA 110 (1408) based on the frequency of the first mechanical beam 124A and the second mechanical beam 124B.

[0138] Although the exemplary operation described above relates 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, the processing circuit 102 may be configured to determine the difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130, and to calculate acceleration based on the difference in resonant frequencies.

[0139] In one or more examples, the accelerometer described herein may implement the functions using hardware, software, firmware, or any combination thereof. Those functions implemented in software may be stored as one or more instructions or code on or transmitted via a computer-readable medium and executed by a hardware-based processing unit. The computer-readable medium may include a computer-readable storage medium corresponding to a tangible medium such as a data storage medium, or a communication medium that includes, for example, any medium facilitating the transfer of a computer program from one place to another according to a communication protocol. Thus, a 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. The data storage medium may be any available medium accessible by one or more computers or one or more processors to retrieve instructions, code, and / or data structures for implementing the techniques described herein.

[0140] Instructions may be executed by or communicatively coupled to one or more processors within the accelerometer. These processors may, for example, include one or more DSPs, general-purpose microprocessors, application-specific integrated circuits (ASICs), FPGAs, or other equivalent integrated or discrete logic circuits. Therefore, the term "processor" as used herein may refer to any of the foregoing structures or any other structure suitable for implementing the techniques described herein. Furthermore, in some aspects, the functionality described herein may be provided within dedicated hardware and / or software modules configured to perform the techniques described herein. Moreover, these techniques may be implemented entirely within one or more circuit or logic elements.

[0141] The techniques disclosed herein can be implemented in various devices or apparatuses including integrated circuits (ICs) or a set of ICs (e.g., chipsets). Various components, modules, or units are described in this disclosure to emphasize functional aspects of a device configured to perform the disclosed techniques, but they do not necessarily need to be implemented by different hardware units. Instead, the various units may be combined with or provided by a collection of interoperable hardware units (including one or more processors as described above) incorporating suitable software and / or firmware.

[0142] Various examples of this disclosure have been described. These and other embodiments are within the scope of the following claims.

Claims

1. A VBA device for a vibrating beam accelerometer, the device comprising: A resonator, the resonator comprising: The first resonator beam and the second resonator beam form a double-ended tuning fork structure; A first driving electrode and a second driving electrode, each configured to receive a single driving voltage, wherein the first driving electrode is located on a first side of the resonator, and the second driving electrode is located on a second side of the resonator opposite to the first side; and First sensing electrode and second sensing electrode, wherein: The first sensing electrode and the second sensing electrode are oriented such that the magnitude of the first capacitance change dC1 / dx of the first sensing electrode relative to displacement is approximately equal to and opposite in sign to the magnitude of the second capacitance change dC2 / dx of the second sensing electrode relative to displacement; and Electrical signal routing: This allows the first sensing output from the first sensing electrode to be subtracted from the second sensing output from the second sensing electrode via a differential amplifier. The electrical signal routing includes: A drive signal path, wherein the drive signal path is coupled to the first drive electrode and the second drive electrode; A first sensing signal path, the first sensing signal path being coupled to the first sensing electrode; and A second sensing signal path, which is coupled to the second sensing electrode. The electrical signal routing is configured to generate: The first parasitic capacitance between the driving signal path and the first sensing signal path generates the first parasitic feedthrough current; and The second parasitic capacitance between the driving signal path and the second sensing signal path generates the second parasitic feedthrough current, such that the magnitudes of the first parasitic feedthrough current and the second parasitic feedthrough current are approximately equal.

2. The device according to claim 1, The first sensing electrode is coupled to the first anchoring comb on the first side of the first resonator beam, and The second sensing electrode is coupled to the second anchoring comb on the second side of the first resonator beam. When the first anchoring comb moves away from the first resonator beam, the first sensing electrode generates a positive current, and When the second anchoring comb moves closer to the first resonator beam, the second sensing electrode generates a positive current.

3. The device of claim 1 further includes a support flexure coupled to the suspended test mass, wherein the support flexure is configured to constrain the out-of-plane movement of the suspended test mass relative to the second plane.

4. The device of claim 1, wherein the resonator is a first resonator, and the device further comprises at least a second resonator, wherein each of the first resonator and the second resonator resonates at a corresponding driving resonant frequency.

5. A method for measuring acceleration based on a vibrating beam accelerometer (VBA), comprising: The processing circuit receives one or more electrical signals from the vibrating beam accelerometer VBA, indicating the frequencies of the first and second resonator beams, wherein the vibrating beam accelerometer VBA includes: A resonator, the resonator comprising: The first resonator beam and the second resonator beam form a double-ended tuning fork structure; A first driving electrode and a second driving electrode, wherein the first driving electrode is located on a first side of the resonator, and the second driving electrode is located on a second side of the resonator opposite to the first side; and First sensing electrode and second sensing electrode, wherein: The first sensing electrode and the second sensing electrode are oriented such that the magnitude of the first capacitance change dC1 / dx of the first sensing electrode relative to displacement is approximately equal to and opposite in sign to the magnitude of the second capacitance change dC2 / dx of the second sensing electrode relative to displacement; and Electrical signal routing: The electrical signal routing includes: A drive signal path, wherein the drive signal path is coupled to the first drive electrode and the second drive electrode; A first sensing signal path, the first sensing signal path being coupled to the first sensing electrode; and A second sensing signal path, which is coupled to the second sensing electrode. The electrical signal routing is configured to generate: The first parasitic capacitance between the driving signal path and the first sensing signal path generates the first parasitic feedthrough current; and The second parasitic capacitance between the driving signal path and the second sensing signal path generates the second parasitic feedthrough current, such that the magnitudes of the first parasitic feedthrough current and the second parasitic feedthrough current are approximately equal. A single driving voltage is received through the first driving electrode and the second driving electrode; The differential amplifier of the vibrating beam accelerometer VBA subtracts the first sensing output from the first sensing electrode from the second sensing output; The processing circuit determines the frequency of the first resonator beam and the frequency of the second resonator beam based on the one or more electrical signals; and The acceleration of the vibrating beam accelerometer VBA is calculated by the processing circuit based on the frequencies of the first resonator beam and the second resonator beam.

6. The method according to claim 5, The first sensing electrode is coupled to the first anchoring comb on the first side of the first resonator beam, and The second sensing electrode is coupled to the second anchoring comb on the second side of the first resonator beam.

7. The method according to claim 6, When the first anchoring comb moves away from the first resonator beam, the first sensing electrode generates a positive current, and When the second anchoring comb moves closer to the first resonator beam, the second sensing electrode generates a positive current.

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