Resonator comprising one or more mechanical beams with additional masses

Abstract

The present disclosure relates to apparatuses, systems, and techniques for determining acceleration of a vibrating beam accelerometer (VBA). For example, a system includes processing circuitry configured to receive, from a first resonator, one or more electrical signals indicative of a frequency of a first mechanical beam and a frequency of a second mechanical beam, determine, based on the one or more electrical signals, the frequency of the first mechanical beam and the frequency of the second mechanical beam, and calculate, based on the frequency of the first mechanical beam and the frequency of the second mechanical beam, an acceleration of a proof mass assembly.

Description

[0001] This application claims the benefit of U.S. Provisional Patent Application No. 62 / 932,298, filed November 7, 2019, which is incorporated by reference herein in its entirety. TECHNICAL FIELD

[0002] The present disclosure relates to a vibrating beam accelerometer. BACKGROUND

[0003] An accelerometer functions by detecting displacement of a proof mass under an inertial force or by detecting the magnitude of force required to prevent displacement of the proof mass. In one example, an accelerometer can detect displacement of a proof mass by a change in frequency of a resonator connected between the proof mass and a supporting base. The resonator can be designed to change in frequency in proportion to a load applied to the resonator by the proof mass under acceleration. The resonator can be electrically coupled to an oscillator circuit or other signal generating circuit, which causes the resonator to vibrate at a resonant frequency. SUMMARY

[0004] Generally, the present disclosure relates to devices, systems, and techniques for determining acceleration of one or more devices. For example, a vibrating beam accelerometer (VBA) described herein can measure a frequency of one or more resonators and calculate an acceleration of the VBA based on a respective frequency of each of the one or more resonators. The resonator can include, for example, a double-ended tuning fork (DETF) structure that includes a pair of mechanical beams. The VBA can induce mechanical vibrations in the pair of mechanical beams such that the mechanical beams vibrate at a resonant frequency. The resonant frequency can vary according to a magnitude of a pressure applied to the resonator or a magnitude of a tension applied to the resonator. The resonator can be connected to a proof mass such that the proof mass is configured to apply tension or pressure to the resonator according to an acceleration of the VBA. In this way, the resonant frequency of the resonator can be related to the acceleration of the VBA, and a processing circuit can be configured to calculate the acceleration of the VBA based on the resonant frequency of the resonator.

[0005] In some examples, a system includes a proof mass assembly including a proof mass, a resonator connection structure, where the resonator connection structure extends parallel to a long axis, a hinge flexure configured to connect the proof mass to the resonator connection structure, where the proof mass rotates about the hinge flexure in response to an acceleration of the system parallel to the long axis of the resonator connection structure, and a first resonator configured to connect the proof mass to the resonator connection structure. The first resonator includes a first mechanical beam extending parallel to the long axis, where the first mechanical beam includes a first mass at a point along the long axis, and a second mechanical beam extending parallel to the long axis, where the second mechanical beam includes a second mass at a point along the long axis. Additionally, the system includes processing circuitry configured to receive, from the first resonator, one or more electrical signals indicative of a frequency of the first mechanical beam and a frequency of the second mechanical beam, determine, based on the one or more electrical signals, the frequency of the first mechanical beam and the frequency of the second mechanical beam, and calculate, based on the frequency of the first mechanical beam and the frequency of the second mechanical beam, an acceleration of the proof mass assembly.

[0006] In some examples, a method includes receiving, by processing circuitry from a first resonator, one or more electrical signals indicative of a frequency of a first mechanical beam and a frequency of a second mechanical beam. A proof mass assembly includes a proof mass, a resonator connection structure, where the resonator connection structure extends parallel to a long axis, a hinge flexure configured to connect the proof mass to the resonator connection structure, where the proof mass rotates about the hinge flexure in response to an acceleration of the system parallel to the long axis of the resonator connection structure, and a first resonator configured to connect the proof mass to the resonator connection structure. The first resonator includes a first mechanical beam extending parallel to the long axis, where the first mechanical beam includes a first mass at a point along the long axis, and a second mechanical beam extending parallel to the long axis, where the second mechanical beam includes a second mass at a point along the long axis. Additionally, the method includes determining, by the processing circuitry and based on the one or more electrical signals, the frequency of the first mechanical beam and the frequency of the second mechanical beam, and calculating, by the processing circuitry and based on the frequency of the first mechanical beam and the frequency of the second mechanical beam, an acceleration of the proof mass assembly.

[0007] In some examples, an apparatus includes a proof mass; a resonator connection structure, wherein the resonator connection structure extends parallel to a long axis; a hinge flexure configured to connect the proof mass to the resonator connection structure, wherein the proof mass rotates about the hinge flexure in response to acceleration of the system parallel to a long axis of the resonator connection structure; and a first resonator configured to connect the proof mass to the resonator connection structure. The first resonator includes a first mechanical beam extending parallel to the long axis, wherein the first mechanical beam includes a first mass at a point along the long axis; and a second mechanical beam extending parallel to the long axis, wherein the second mechanical beam includes a second mass at a point along the long axis. The first resonator is configured to output one or more electrical signals indicative of a frequency of the first mechanical beam and a frequency of the second mechanical beam.

[0008] This summary is intended to provide an overview of the subject matter described in this disclosure. It is not intended to provide an exclusive or exhaustive explanation of the systems, apparatuses, and methods described in detail in the following description. Further details of one or more examples of this disclosure are set forth in the accompanying drawings and description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims. BRIEF DESCRIPTION OF DRAWINGS

[0009] FIG. 1 is a block diagram illustrating an accelerometer system in accordance with one or more techniques of this disclosure.

[0010] FIG. 2 is a conceptual diagram illustrating a vibrating beam accelerometer (VBA) in accordance with one or more techniques of this disclosure.

[0011] FIG. 3A is a conceptual diagram illustrating a VBA including a support flexure and having a resonator in accordance with one or more techniques of this disclosure.

[0012] FIG. 3B is a conceptual diagram illustrating a cross-sectional view of a VBA having a support flexure and having a resonator in accordance with one or more techniques of this disclosure.

[0013] FIG. 4A is a conceptual diagram illustrating a first resonator having an additional mass in accordance with one or more techniques of this disclosure.

[0014] FIG. 4B is a conceptual diagram illustrating a portion of a first resonator of including an additional mass in accordance with one or more techniques of this disclosure. FIG. 4A

[0015] FIG. 5A ​is a conceptual diagram illustrating a second resonator including a gap according to one or more techniques of the present disclosure.

[0016] FIG. 5B is a conceptual diagram illustrating a portion of a second resonator including a gap according to one or more techniques of the present disclosure. FIG. 5A

[0017] FIG. 6 is a graph illustrating a first plot and a second plot according to one or more techniques of the present disclosure, the first plot representing a quadratic nonlinearity coefficient as a function of an additional mass position, the second plot representing a zero acceleration resonance frequency difference as a function of an additional mass position.

[0018] FIG. 7 is a flowchart illustrating example operations for determining an acceleration of a VBA according to one or more techniques of the present disclosure.

[0019] Like reference characters indicate like elements throughout the specification and drawings. DETAILED DESCRIPTION

[0020] The present disclosure relates to apparatuses, systems, and techniques for determining an acceleration of a vibrating beam accelerometer (VBA). For example, the present disclosure relates to a VBA having an in-plane proof mass. A VBA configured according to techniques of the present disclosure can include at least one or more resonators, a planar geometry, a single primary mechanical anchor between the support base and the VBA, resonator connection structures connecting the resonators to the single primary anchor, and a hinge flexure mechanically connecting the proof mass to the single primary anchor. One or more techniques of the present disclosure provide that a mechanical beam of a resonator can include additional masses and / or form a gap, which affect a respective resonance frequency of the resonator and affect a relationship between the respective resonance frequency and an acceleration of the VBA.

[0021] ​In some examples, the VBA can include a first resonator and a second resonator, where the first resonator and the second resonator are each connected to the proof mass. For example, the first resonator and the second resonator can be connected to the proof mass such that the proof mass applies tension to the first resonator when the proof mass applies pressure to the second resonator, and the proof mass applies pressure to the first resonator when the proof mass applies tension to the second resonator. In some cases, the processing circuitry can be configured to calculate a difference between a resonant frequency of the first resonator and a resonant frequency of the second resonator, and calculate an acceleration of the VBA based on the difference. For example, the difference between the resonant frequency of the first resonator and the resonant frequency of the second resonator can have an approximately linear relationship with the acceleration of the VBA. For example, the relationship can include a quadratic nonlinearity coefficient (K2) representing a non-linear relationship between the difference in resonant frequencies and the acceleration of the VBA.

[0022] In some examples, the first resonator can include a first mechanical beam and a second mechanical beam, and the second resonator can include a third mechanical beam and a fourth mechanical beam. The first mechanical beam and the second mechanical beam can each include one or more “additional masses,” where the respective additional masses affect a resonant frequency and a quadratic nonlinearity coefficient of the first resonator. The third mechanical beam and the fourth mechanical beam can each include one or more gaps, while the additional masses are located on the first mechanical beam and the second mechanical beam. For example, the first resonator and the second resonator can be substantially identical, except that the second resonator forms a gap in one or more locations, while the first resonator includes the additional masses.

[0023] The techniques of this disclosure can provide one or more advantages. For example, the respective additional masses included by the first mechanical beam and the second mechanical beam, and the respective gaps formed by the third mechanical beam and the fourth mechanical beam, can ensure that a quadratic nonlinearity coefficient corresponding to a relationship between the difference in resonant frequencies and the acceleration of the VBA is zero or close to zero (e.g., less than 5 micrograms per gram squared (pg / g 2 ). A system with a quadratic nonlinearity coefficient of zero or close to zero can be advantageous for accurately calculating the acceleration of the VBA compared to a system with a quadratic nonlinearity coefficient greater than the quadratic nonlinearity coefficient of the VBA described herein. Additionally, the respective additional masses and gaps formed by the mechanical beams can ensure that the difference between the resonant frequency of the first resonator and the resonant frequency of the second resonator is not zero when the acceleration of the VBA is zero meters per second squared (m / s 2 ). It can be advantageous for the difference in the respective resonant frequencies of the first resonator and the second resonator at zero acceleration to not be zero, in order to reduce interference between the first resonator and the second resonator, compared to a system where the difference in the respective resonant frequencies of the first resonator and the second resonator at zero acceleration is zero or closer to zero than the system described herein.

[0024] FIG. 1 This is a block diagram illustrating an accelerometer system 100 according to one or more technologies of this disclosure. FIG. 1 As shown, the accelerometer system 100 includes a processing circuit 102, resonator drive circuits 104A to 104B (collectively referred to as "resonator drive circuit 104"), and a test mass assembly 110. The test mass assembly 110 includes a test mass 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").

[0025] In some examples, the accelerometer system 100 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. FIG. 1 (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 104A and the resonator drive circuit 104B, 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 102 may determine the acceleration of the object based on the first set of sensing signals and the second set of sensing signals.

[0026] In some examples, processing circuitry 102 may include one or more processors configured to implement functions and / or processing instructions for execution within accelerometer system 100. For example, processing circuitry 102 may be capable of processing instructions stored in a storage device. Processing circuitry 102 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. Therefore, processing circuitry 102 may include any suitable structure, whether in hardware, software, firmware, or any combination thereof, to perform the functions described herein for processing circuitry 102.

[0027] Memory ( FIG. 1The memory (not shown in FIG. 1) can be configured to store information within the accelerometer system 100 during operation. The memory can include a computer-readable storage medium or computer-readable storage device. In some examples, the memory includes one or more of a short-term memory or a long-term memory. The memory can include, for example, random access memory (RAM), dynamic random access memory (DRAM), static random access memory (SRAM), magnetic discs, optical discs, flash memory, or forms of electrically programmable memory (EPROM) or electrically erasable and programmable memory (EEPROM). In some examples, the memory is used to store program instructions for execution by the processing circuit 102.

[0028] In some examples, the resonator drive circuit 104A can be electrically coupled to the first resonator 120. The resonator drive circuit 104A can output a first set of drive signals to the first resonator 120 such that the first resonator 120 vibrates at a resonant frequency. Additionally, in some examples, the resonator drive circuit 104A can receive a first set of sense signals from the first resonator 120, where the first set of sense signals can be indicative of a mechanical vibration frequency of the first resonator 120. The resonator drive circuit 104A can output the first set of sense signals to the processing circuit 102 for analysis. In some examples, the first set of sense signals can represent a data stream such that the processing circuit 102 can determine the mechanical vibration frequency of the first resonator 120 in real-time or near real-time.

[0029] In some examples, the resonator drive circuit 104B can be electrically coupled to the second resonator 130. The resonator drive circuit 104B can output a second set of drive signals to the second resonator 130 such that the second resonator 130 vibrates at a resonant frequency. Additionally, in some examples, the resonator drive circuit 104B can receive a second set of sense signals from the second resonator 130, where the second set of sense signals can be indicative of a mechanical vibration frequency of the first resonator 130. The resonator drive circuit 104B can output the second set of sense signals to the processing circuit 102 for analysis. In some examples, the second set of sense signals can represent a data stream such that the processing circuit 102 can determine the mechanical vibration frequency of the second resonator 130 in real-time or near real-time.

[0030] The proof mass assembly 110 can use the first resonator 120 and the second resonator 130 to secure the proof mass 112 to the resonator connection structure 116. For example, the proof mass 112 can be secured to the resonator connection structure 116 in a first direction using the hinge flexure 114. The proof mass 112 can be secured to the resonator connection structure 116 in a second direction using the first resonator 120 and the second resonator 130. The proof mass 112 can be configured to pivot about the hinge flexure 114, thereby applying a compressive force to the first resonator 120 and a tensile force to the second resonator 130 in the second direction. For example, if the proof mass 112 pivots toward the first resonator 120, the proof mass 112 applies a compressive force to the first resonator 120 and a tensile force to the second resonator 130. If the proof mass 112 pivots toward the second resonator 130, the proof mass 112 applies a tensile force to the first resonator 120 and a compressive force to the second resonator 130.

[0031] The acceleration of the proof mass assembly 110 can affect the degree to which the proof mass 112 pivots about the hinge flexure 114. As such, 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 proof mass assembly 110. The amount of force (e.g., compressive or tensile) applied to the resonators 120, 130 can be related to an acceleration vector of the proof mass assembly 110, where the acceleration vector is perpendicular to the hinge flexure 114.

[0032] In some examples, the magnitude of the force applied to the first resonator 120 can be related to a resonant frequency at which the first resonator 120 vibrates in response to the resonator drive circuit 104A outputting the first set of drive signals to the first resonator 120. For example, the first resonator 120 can include mechanical beams 124. As such, the first resonator 120 can represent a double-ended tuning fork (DETF) structure, where each of the mechanical beams 124 vibrates at a resonant frequency in response to receiving the first set of drive signals. The electrodes 128 can generate electrical signals indicative of the mechanical vibration frequency of the first mechanical beam 124A and the mechanical vibration frequency of the second mechanical beam 124B. For example, a first set of electrodes 128A can generate a first electrical signal, a second set of electrodes 128B can generate a second electrical signal, and a third set of electrodes 128C can generate a third electrical signal. The electrodes 128 can output the first electrical signal, the second electrical signal, and the third electrical signal to the processing circuit 102.

[0033] The processing circuit 102 can determine a difference between the first electrical signal and the second electrical signal, and determine a mechanical vibration frequency of the first mechanical beam 124A based on the difference between the first electrical signal and the second electrical signal. Additionally or alternatively, the processing circuit 102 can determine a difference between the second electrical signal and the third electrical signal, and determine a mechanical vibration frequency of the second mechanical beam 124B based on the difference between the second electrical signal and the third electrical signal. In some examples, the mechanical vibration frequencies of the first mechanical beam 124A and the second mechanical beam 124B are substantially the same when the first set of drive signals are output by the resonator drive circuit 104A to the first resonator 120. For example, the mechanical vibration frequency of the first mechanical beam 124A and the mechanical vibration frequency of the second mechanical beam 124B can each represent a resonant frequency of the first resonator 120, where the resonant frequency is related to a magnitude of the force applied to the first resonator 120 by the proof mass 112. The magnitude of the force applied to the first resonator 120 by the proof mass 112 can be related to an acceleration of the proof mass assembly 110 relative to the long axis of the resonator connection structure 116. As such, the processing circuit 102 can calculate the acceleration of the proof mass 112 relative to the long axis of the resonator connection structure 116 based on the detected mechanical vibration frequencies of the mechanical beams 124.

[0034] In some examples, the magnitude of the force applied to the second resonator 130 can be related to a resonant frequency at which the second resonator 130 vibrates in response to the second set of drive signals being output by the resonator drive circuit 104B to the second resonator 130. For example, the second resonator 130 can include mechanical beams 134. As such, the second resonator 130 can represent a double-ended tuning fork (DETF) structure, where each of the mechanical beams 134 vibrates at a resonant frequency in response to receiving the second set of drive signals. The electrodes 138 can generate electrical signals indicative of the mechanical vibration frequency of the third mechanical beam 134A and the mechanical vibration frequency of the fourth mechanical beam 134B. For example, a fourth set of electrodes 138A can generate a fourth electrical signal, a fifth set of electrodes 138B can generate a fifth electrical signal, and a sixth set of electrodes 138C can generate a sixth electrical signal. The electrodes 138 can output the fourth electrical signal, the fifth electrical signal, and the sixth electrical signal to the processing circuit 102.

[0035] The processing circuit 102 can determine a difference between the fourth electrical signal and the fifth electrical signal, and determine a mechanical vibration frequency of the third mechanical beam 134A based on the difference between the fourth electrical signal and the fifth electrical signal. Additionally or alternatively, the processing circuit 102 can determine a difference between the fifth electrical signal and the sixth electrical signal, and determine a mechanical vibration frequency of the fourth mechanical beam 134B based on the difference between the fifth electrical signal and the sixth electrical signal. In some examples, the mechanical vibration frequencies of the third mechanical beam 134A and the fourth mechanical beam 134B are substantially the same when the second set of drive signals is output by the resonator drive circuit 104B to the second resonator 130. For example, the mechanical vibration frequency of the third mechanical beam 134A and the mechanical vibration frequency of the fourth mechanical beam 134B can each represent a resonant frequency of the second resonator 130, where the resonant frequency is related to a magnitude of the force applied to the second resonator 130 by the proof mass 112. The magnitude of the force applied to the second resonator 130 by the proof mass 112 can be related to an acceleration of the proof mass assembly 110 relative to the long axis of the resonator connection structure 116. As such, the processing circuit 102 can calculate the acceleration of the proof mass 112 relative to the long axis of the resonator connection structure 116 based on the detected mechanical vibration frequencies of the mechanical beams 134.

[0036] In some cases, the processing circuit 102 can calculate the acceleration of the proof mass assembly 110 relative to the long axis of the resonator connection structure 116 based on a 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 proof mass assembly 110 accelerates in a first direction along the long axis of the resonator connection structure 116, the proof mass 112 pivots toward the first resonator 120 such that the proof mass 112 applies a compressive force to the first resonator 120 and a tensile force to the second resonator 130. When the proof mass assembly 110 accelerates in a second direction along the long axis of the resonator connection structure 116, the proof mass 112 pivots toward the second resonator 130 such that the proof 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 to which the first compressive force is applied can be greater than the resonant frequency of the resonator to which the second compressive force is applied. When the first tensile force is greater than the second tensile force, the resonant frequency of the resonator to which the first tensile force is applied can be greater than the resonant frequency of the resonator to which the second tensile force is applied.

[0037] Although the accelerometer system 100 is shown as including the resonator connection structure 116, in some examples, the resonator connection structure 116 can be omitted. FIG. 1In some examples not shown, the proof mass 112, the first resonator 120, and the second resonator 130 are not connected to the resonator connection structure. In some such examples, the proof mass 112, the first resonator 120, and the second resonator 130 are connected to a base. For example, the hinge flexure 114 can secure the proof mass 112 to the base such that the proof mass 112 can pivot about the hinge flexure 114, thereby exerting tension and / or compression forces on the first resonator 120 and the second resonator 130.

[0038] In some examples, a difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130 can have an approximately linear relationship with an acceleration of the proof mass assembly 110. In some examples, a relationship between the difference in resonant frequencies of the resonators 120, 130 and the acceleration of the proof mass assembly 110 can not be perfectly linear. For example, the relationship can include a quadratic nonlinearity coefficient (K2) representing a nonlinear relationship between the difference in resonant frequencies of the resonators 120, 130 and the acceleration of the proof mass assembly 110. It can be advantageous for the quadratic nonlinearity coefficient to be zero or close to zero such that the processing circuit 102 is configured to accurately determine the acceleration of the proof mass assembly 110 based on the relationship between the difference in resonant frequencies of the resonators 120, 130 and the acceleration of the proof mass assembly 110. One type of common mode error is a vibration rectification error (VRE). VRE can occur as a change in zero gravity output or accelerometer bias that occurs during vibration. VRE can be caused by nonlinearities in the accelerometer input to output transfer function. Typically, the most dominant source is the quadratic nonlinearity coefficient (K2). To avoid false vibrations, mitigating this quadratic nonlinearity can be beneficial.

[0039] Additionally, it can be advantageous for the difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130 to not be zero when the acceleration of the proof mass assembly 110 is 0 m / s 2 when the proof mass assembly 110 is not accelerating. This can be advantageous to reduce interference between the first resonator and the second resonator when the difference in the respective resonant frequencies of the resonators 120, 130 is not zero.

[0040] In some examples, the accelerometer system 100 can ensure that the quadratic nonlinearity coefficient is close to zero, and ensure that the zero acceleration difference of the respective resonant frequencies of the resonators 120, 130 is not zero by including additional masses on the first resonator 120. For example, the first mechanical beam 124A and the second mechanical beam 124B can each include one or more additional masses, where the one or more additional masses affect the resonant frequency and the quadratic nonlinearity coefficient of the first resonator 120. The third mechanical beam 134A and the fourth mechanical beam 134B can each form one or more gaps, while the additional masses are located on the first mechanical beam 124A and the second mechanical beam 124B. In some examples, the first resonator 120 and the second resonator 130 are substantially identical, except that the first resonator 120 includes additional masses on the first mechanical beam 124A and the second mechanical beam 124B, while the third mechanical beam 134A includes a gap corresponding to the additional mass on the first mechanical beam 124A, and the fourth mechanical beam 134B includes a gap corresponding to the additional mass on the second mechanical beam 124B. Such differences between the first resonator 120 and the second resonator 130 can ensure that the quadratic nonlinearity coefficient is close to zero (e.g., less than 5 pg / g 2 ), and ensure that the zero acceleration difference of the respective resonant frequencies of the resonators 120, 130 is not zero.

[0041] For a VBA with two identical resonators, even order nonlinearities (e.g., quadratic nonlinearity, fourth order nonlinearity) are common mode error sources that are nominally cancelled out by the differential output. However, mismatched resonators, such as the first resonator 120 and the second resonator 130, can cause K2 of the accelerometer to not necessarily be set to zero. Mismatched resonators can be needed to avoid operating the two resonators at the same frequency. Driving two resonators at similar frequencies can cause the resonators to interfere with each other (mechanical and electrical interference), which ultimately degrades the output of the VBA. The resonators 120 and 130 can ensure that K2 is zero or close to zero, and reduce such interference that degrades the output of the VBA.

[0042] Although the accelerometer system 100 is described as having two resonators, in other examples not shown in FIG. 1 , the accelerometer system can include fewer than two resonators or more than two resonators. For example, one type of accelerometer system can include one resonator. Another type of accelerometer system can include four resonators.

[0043] FIG. 2 is a conceptual diagram illustrating a VBA 110 in accordance with one or more techniques of the present disclosure. For example, FIG. 2A top view of a VBA 110 including a proof mass 112, a hinge flexure 114, an anchor 115, a resonator connection structure 116, a first resonator 120, and a second resonator 130 is shown. The VBA 110 can be an example of a proof mass assembly 110 of FIG. 1

[0044] The VBA 110 includes a proof mass 112 connected to a rigid resonator connection structure 116 at a hinge flexure 114, and resonators 120, 130. For a VBA according to the present disclosure, the proof mass 112 is movable in a plane parallel to the plane of a support base (not shown). The support base can be, for example, a quartz or silicon wafer substrate. The resonators 120, 130 of the VBA 110 convert the inertial force of the proof mass 112 under acceleration to a change in the drive resonant frequency. The VBA outputs the change in the resonant frequency of each resonator as an indication of the amount of acceleration. In some examples, the resonators can be located in the vicinity of the mass such that the resonators receive the force of the mass amplified by leverage. FIG. 2

[0045] In an example of a MEMS VBA, the VBA 110 can be made from a dissolved wafer process that produces the VBA 110 as a silicon mechanical structure tethered to a lower glass substrate and an upper glass substrate (not shown) at specific anchor regions, such as the anchor 115. The glass substrates can be etched in other regions to define release regions of the VBA 110 that include air gaps that free silicon portions, such as the proof mass 112, to move freely relative to the substrate. The unetched regions are bonded to the silicon to define mechanical anchors. The geometry of both the silicon mechanism and the anchor regions can be defined by photolithography. FIG. 2 The dissolved wafer process of making a silicon VBA and glass substrates is merely one example of a technique of making a VBA of the present disclosure. Other techniques can be used to make the geometry of the VBA 110. Other examples can include materials such as quartz (Si02), piezoelectric materials, and similar materials. Other processes can include isotropic etching, chemical etching, deep reactive ion etching (DRIE), and similar processes. In examples where the proof mass 112, resonator connection structure 116, hinge flexure 114, resonators 120, 130 are constructed of a single piece of material, this results in all of the components of the VBA 110 having the same coefficient of thermal expansion (CTE). All of the components of the VBA 110 are in the same plane parallel to the X-Y plane as shown in

[0046] FIG. 2 FIG. 2

[0047] ​​​​​The test mass 112 is connected to the resonator connection structure 116 at the anchor 115 via a hinge flexure 114. The point where the hinge flexure 114 connects to the anchor 115 is the rotation center of the test mass 112. The first resonator 120 and the second resonator 130 are connected to the same main anchor 115 via the rigid resonator connection structure 116. The resonators 120 and 130 are connected to the test mass 112 at a distance r1 from the rotation center of the test mass 112. The distance r2 between the center of mass 113 of the test mass 112 and the rotation center of the test mass 112. This causes the inertial force of the test mass 112 to be amplified by a leverage ratio r2 / r1.

[0048] In other words, the hinge flexure 114 can be configured to flexibly connect the test mass block 112 to the resonator connection structure 116. The hinge flexure 114 holds the test mass block 112 parallel to the support base. FIG. 2 (Not shown in the image) Suspended at anchor 115. In response to the acceleration of VBA 110, the test mass 112 rotates in its plane about the hinge flexure 114, which is parallel to the XY plane and parallel to the support base (…). FIG. 2 (Not shown in the image). The support base of this disclosure can be formed from a substrate using the above-described etching process.

[0049] exist FIG. 2 In the examples, resonators 120 and 130 include anchoring combs and mechanical beams with release combs. The first resonator 120 includes a mechanical beam 124 with release combs and anchoring combs 122A to 122C (collectively referred to as "anchoring combs 122"), and the second resonator 130 includes a mechanical beam 134 with release combs and anchoring combs 132A to 132C (collectively referred to as "anchoring combs 132"). In some examples, the anchoring combs may be referred to as stator combs. Resonators 120 and 130 are configured to flexibly connect a test mass block 112 to the resonator connection structure 116 and to flex in the plane of the test mass block 112 based on rotation of the test mass block 112 about the hinge flexure 114.

[0050] In some examples, the anchoring comb 122A may include a first set of electrodes configured to generate a first electrical signal. FIG. 2 (Not shown in the image), the anchoring comb 122B may include a second set of electrodes configured to generate a second electrical signal. FIG. 2 (not shown in the image), and the anchoring comb 122C may include a third set of electrodes configured to generate a third electrical signal ( FIG. 2 (Not shown in the image). In some examples, the anchor comb 132A may include a fourth set of electrodes configured to generate a fourth electrical signal. FIG. 2 (Not shown in the image), the anchoring comb 132B may include a fifth set of electrodes configured to generate a fifth electrical signal.FIG. 2 (Not shown in the image), and the anchoring comb 132C may include a sixth set of electrodes configured to generate a sixth electrical signal. FIG. 2 (Not shown in the image). Resonators 120 and 130 can output the first, second, third, fourth, fifth, and sixth electrical signals to the processing circuit. FIG. 2 (Not shown in the image), the processing circuit is configured to calculate the acceleration of the VBA 110 based on these electrical signals.

[0051] Each of the two resonators 120 and 130 resonates at a corresponding resonant frequency. In some examples, the first resonator 120 has an acceleration of zero m / s² at VBA 110. 2 The resonant frequency at which the second resonator 130 is 0 m / s² is the same as the acceleration of the second resonator 130 at VBA 110. 2 The difference between the resonant frequencies at those times is not zero. VBA 110 includes deposition onto a glass substrate ( FIG. 2 Metal layers (not shown) are defined on the VBA 110. These metal layers define wires that connect silicon electrodes to bonding pads. The bonding pads are external to the VBA 110 and are used for electrical connection to external circuitry that excites and sustains the mechanical motion of each resonator of the resonators 120, 130 at its resonant frequency via electrostatic actuation (e.g., by applying a charge). In the presence of external acceleration, the test mass 112 deflects and applies an axial force to the mechanical beams 124 and 134 (collectively referred to as "mechanical beams 124, 134") of the resonators 120, 130. This axial force from the test mass 112 causes a change in the driving resonant frequency, such that the frequency change can be used to measure the external acceleration on the VBA 110.

[0052] The release combs on mechanical beams 124 and 134, the anchoring comb 132, and the teeth on the anchoring comb 122 enable the detection of changes in resonant frequency, which can be converted into the magnitude of a force (e.g., an increase or decrease in force) and further converted into the acceleration of VBA 110. For example, during calibration, the frequency change can represent the magnitude of the force applied to the respective mechanical beams 124 and 134. The processing circuitry can then calculate the acceleration of VBA 110 based on the magnitude of the force applied to the mechanical beams. FIG. 3A In the example, when a force (e.g., pressure or tension) is applied to the mechanical beams 124, 134 by rotating the test mass block 112, the two resonators 120, 130 can allow difference frequency measurements caused by frequency variations.

[0053] The difference frequency measurement from the sense signal output from the VBA 110 is used to suppress error sources common to both resonators. One example can include temperature variations. That is, changes in operating conditions, such as temperature variations, can affect both resonators in the same way. A second example would be any offset in the voltage applied to both resonators. The difference frequency measurement can subtract the common error sources applied to both resonators by subtracting the common error and leaving only the signal caused by the acceleration on the VBA 110. The difference frequency measurement can then ultimately result in an improvement in the zero bias repeatability of the accelerometer.

[0054] In some examples, the resonators can have different resonant frequencies, for example, the first resonator 120 can be configured to resonate at a different frequency than the second resonator 130. In some examples, the mass of one resonator can be configured differently than one or more other resonators. A VBA with resonators having different resonant frequencies can provide benefits, for example, when the gravity of the VBA is zero, that is, the VBA is experiencing substantially no acceleration, the resonators can not vibrate at exactly the same frequency. The different frequencies at zero gravity result in an intentional offset in the VBA and can improve detectability and performance.

[0055] In FIG. 2 examples, two resonators are used to provide a difference frequency measurement. In other examples, the techniques of the present disclosure can also be applied to VBAs with more or fewer resonators. In other examples, one or more resonators can be oriented at any angle, not just x and y, while still using the techniques of the present disclosure. Although shown in FIG. 3A examples as double-ended tuning fork (DETF) comb resonators, in other examples, the resonators 120, 130 can be configured as other types of resonators. For example, one or both of the resonators 120, 130 can include a single mechanical beam or more complex resonator geometry instead of a DETF. Additionally, the mechanical beams 124, 134 can include piezoelectric material and can not include comb teeth.

[0056] In examples of the VBA 110, the resonators 120, 130 can be configured to be able to flex in a direction substantially parallel to the long axis of the resonator connection structure 116. In FIG. 1 examples, the long axis of the resonator connection structure 116 is parallel to the X axis. In examples of the VBA 110, the resonators 120, 130 are oriented along the X axis. In the present disclosure, substantially parallel means that the structures or planes are parallel within manufacturing and measurement tolerances.

[0057] The resonator connection structure 116 connects the resonators 120, 130 to the primary anchor 115 with a sufficiently rigid connection that allows the proof mass 112 to exert an axial force on the mechanical beams 124, 134. The resonator connection structure 116 is sized to have a stiffness that is greater than the axial spring constant of the resonators. The geometry of the resonator connection structure 116 and the resonators 120, 130 according to the techniques of the present disclosure can configure the proof mass 112, the mechanical beams 124, 134, and the resonator connection structure 116 to be connected to the support base through the anchor 115. The resonator connection structure 116 can reduce or prevent bias errors that can be caused by a thermal expansion mismatch between the glass substrate (support base) and the silicon mechanism (e.g., the proof mass 112). In other words, the design of the silicon and glass masks allows both the proof mass 112 and the resonators 120, 130 to be primarily anchored to a single region, e.g., at the anchor 115.

[0058] Advantages of the geometry of the VBA of the present disclosure can include reducing or preventing thermal expansion mismatches, as well as other forces exerted on the substrate from reaching the resonators 120, 130 and causing significant deflection of the mechanical beams 124, 134. The geometry of the present disclosure can have the advantage of ultimately providing more accurate external acceleration measurements compared to VBA’s with different geometries. In other words, in an example where a first thermal expansion is different than a second thermal expansion, the anchor 115 can be configured to allow the first thermal expansion of the support base, as well as the second thermal expansion of the monolithic material of the resonators 120, 130 and the resonator connection structure 116. The geometry of the resonator connection structure 116 is configured to substantially prevent other forces exerted to the support base from being transferred to the proof mass 112 or at least two resonators. Some examples of other forces can include forces exerted to the VBA 110 by a circuit board or other structure on which the VBA 110 is mounted. The circuit board can be subjected to forces such as crushing or twisting, which can be transferred to components on the circuit board, including the VBA 110.

[0059] FIG. 1 is a conceptual diagram illustrating a VBA 300 including a support flexure and having resonators according to one or more techniques of the present disclosure. Similar to FIG. 1 , FIG. 1 is a top view of the VBA 300 illustrating the anchor 315 to the support base, but the support base is not shown. The VBA 300 includes a proof mass 312 connected to the anchor 315 and a resonator connection structure 316 at a hinge flexure 314, as well as a first resonator 320 and a second resonator 330 (collectively, “resonators 320, 330”). The proof mass 312 can be similar to FIG. 1The proof mass 312 is substantially identical to the proof mass 112, except that the proof mass 312 is configured to interact with one or more support flexures to enhance movement of the proof mass 312 in the out-of-plane (z) direction. The hinge flexure 314 can be an example of the hinge flexure 114 FIG. 3A The resonator connection structure 316 can be an example of the resonator connection structure 116 FIG. 2 The first resonator 320 can be an example of the first resonator 120 FIG. 2 The second resonator 330 can be an example of the second resonator 130 FIG. 3A Also shown is a cross-section A-A' extending along the long axis of the resonator connection structure 316 and through the anchor 315. FIG. 3A Also shown is a cross-section A-A' extending along the long axis of the resonator connection structure 316 and through the anchor 315.

[0060] The proof mass 312 includes support flexures, but otherwise the function and description of the proof mass 312 is the same as described above with respect to the proof mass 112 FIG. 2 For example, the proof mass 312 is connected to the resonator connection structure 316 at the anchor 315 by the hinge flexure 314. The point at which the hinge flexure 314 connects to the anchor 315 is the center of rotation of the proof mass 312. The resonators 320, 330 are connected to the same primary anchor 315 by the resonator connection structure 316. The resonators 18A and 18B are connected to the proof mass 312 at a distance ri from the center of rotation of the proof mass 312. The center of mass 313 of the proof mass 312 is at a distance r2from the center of rotation of the proof mass 312. As with the VBA 110 shown in FIG. 2 This results in the inertial forces on the mechanical beams 324, 334 of the proof mass 312 being amplified by a lever ratio of r2 / ri, as with the VBA 110 shown in

[0061] The proof mass 312 can include one or more support flexures to enhance movement of the proof mass 312 in the out-of-plane (z) direction. In other words, the support flexures (e.g., flexures 342) coupled to the proof mass 312 are configured to limit out-of-plane motion of the proof mass relative to the X-Y plane parallel to the proof mass 312 and the resonator connection structure 316. These flexures are configured to be substantially 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, the flexures 342 include a support base (e.g., a flexure base 344) connected to the proof mass 312 similar to the primary anchor 315 FIG. 3BThe flexure 342 can include a flexible portion 346C connected between the anchor portion 344C and the proof mass 312. The flexible portion 346C can have the same or similar material as the proof mass 312. The configuration of the one or more support flexures can reduce out-of-plane movement while avoiding biasing caused by forces applied to the accelerometer mechanism (e.g., the proof mass 312 and the resonators 18A and 18B) that can be caused by CTE mismatch between the substrate and the accelerometer mechanism.

[0062] The proof mass 312 can include additional support flexures, such as flexures having anchor portions 344A and 344B and flexible portions 346A and 346B. As described above for the flexure 342, the flexible portions 346A and 346B can have the same or similar material as the proof mass 312. FIG. 3B The locations of the anchor portions 344A and 344B and the shapes and configurations of the flexible portions 346A and 346B shown in FIG. 3 are merely one example technique for providing support flexures to stiffen the movement of the proof mass 312 in the out-of-plane (z) direction. In other examples, the flexible portions 346A and 346B can have different shapes, such as straight beams or S-shapes. In other examples, the VBA 300 can have more or fewer support flexures. The anchor portions of the support flexures of the present disclosure can be configured to not exert significant forces on the proof mass 312, so the mechanism of the VBA 300 can still be primarily connected to the structure of the support base through a single anchor region (e.g., the anchor 315). As described above with respect to the VBA 110, FIG. 3B As with the VBA 110 described above, advantages of the geometry of the VBA 300 include reducing bias errors that can be caused by thermal expansion mismatch between the glass substrate (support base) and the silicon mechanism (e.g., the proof mass 312).

[0063] As described above with respect to the VBA 110, FIG. 2 Using a single primary mechanical anchor can reduce or prevent bias errors that can be caused by external mechanical forces applied to the circuit board, package, and / or substrate (including the accelerometer mechanism). Since the sources of these forces can be unavoidable (e.g., thermal expansion mismatch between the substrate and the mechanism), the geometry of the VBA of the present disclosure can mechanically isolate the sensitive components. Another advantage can include reducing cost and complexity by implementing mechanical isolation within the MEMS mechanism, which can avoid the need for additional manufacturing steps or components, such as discrete isolation stages.

[0064] FIG. 3A is a conceptual diagram showing a cross-sectional view of a VBA with support flexures and with resonators, in accordance with one or more techniques of the present disclosure. FIG. 3BA cross-section A-A’ is shown extending down the long axis of the resonator connection structure 316 and through the anchor 315. FIG. 3B Parts having the same reference numbers in FIG. 2 and FIG. 3B have the same descriptions, properties, and functions as described above. For example, the VBA 300 includes a proof mass 312 connected to the resonator connection structure 316 at an anchor 315 (not shown in FIG. 3B ). FIG. 2 Anchor portions of the anchor combs 122C and 132C are also shown, as well as anchor portions supporting flexures 344A and 344B.

[0065] As described above with respect to FIG. 3B , the VBA 300 can be fabricated using a silicon mask and a glass mask such that both the proof mass 312 and the resonator connection structure 316 are primarily anchored at a single region, such as at the anchor 315. The released silicon mechanical structure of the VBA 300 can be tethered to a support base 346, which can be a glass substrate, such as a quartz substrate or a silicon substrate. The proof mass 312 can also be tethered at other anchor regions, such as anchor portions 344A and 344B, that are configured to allow the released silicon portions, such as the proof mass 312 and the mechanical beams 324 and 334 of the resonators 320, 330 (not shown in FIG. 3B ), to move freely with respect to the support base 346.

[0066] The support base 346 can include an encapsulation structure, such as structures 348A and 348B, that can surround the released portions of the VBA 300. In some examples, the VBA 300 can include a lower support base 346 and an upper support (not shown in FIG. 2 ). In some examples, the anchor portions, such as the anchor 315, can be mechanically connected to both the lower support base 346 and the upper support. The support base 346 can define a second plane that is also substantially parallel to the X-Y plane, which is different from the plane of the released portions of the VBA 300. The plane defined by the released portions of the VBA 300, such as the mechanical beams 324, 334 and the proof mass 312, can be substantially parallel to the second plane defined by the support base 346. As described above with respect to FIG. 2 , the air gap between the plane of the proof mass and the plane of the support base 346 can allow the silicon portions, such as the proof mass, to move freely with respect to the substrate.

[0067] The resonator connection structure 316 can be configured to be more rigid than the resonator. The rigid structure of the resonator connection structure 316 is connected to the resonator and branches back to the primary mechanical anchor 315, which is connected to the support base 346. As described above, the resonator connection structure 316 is sized to have a stiffness greater than the axial spring constant of the resonator and to support the resonator in the in-plane (e.g., x and y) directions. In some examples, the resonator connection structure 316 can be an order of magnitude stiffer than the mechanical beams 324, 334. The single primary anchor 315 allows for mechanical connection of the free portion of the VBA 300 to thermally expand at different rates or directions of the support base 346 without being constrained by other connections of the support base 346 that can cause biasing and inaccuracy.

[0068] The support base 346 can include metal layers deposited onto a glass substrate (not shown in FIG. 3A ). In some examples, the support base 346 can include bond pads and other metal structures (e.g., as shown by the arrows from the support base 346) on a bottom surface of the support base 346, such as the conductive paths 350A and 350B. In some examples, the support base 346 can include metal layers on a top surface (e.g., on a surface opposite the bottom surface), and in other examples, the support base 346 can include intermediate metal layers (not shown in FIG. 3B ) between the top and bottom surfaces. In some examples, the metal layers can be electrically connected to each other with vias or other types of connections through the support base 346. In some examples, the electrical wires can also be defined by other conductive materials other than metal. As described above with respect to FIG. 2 , the metal layers or other conductive materials can define electrical paths for carrying signals to and from the VBA 300, such as the conductive paths 350A and 350B.

[0069] As described above with respect to FIG. 3A and FIG. 4A , each of the one or more resonators can include a mechanical beam (e.g., the mechanical beam 324) with a free comb and an anchor comb (e.g., 122C and 132C). As FIG. 1 to FIG. 2 shown, the anchor portions of the anchor combs 122C and 132C extend from the plane of the support base 346 to the plane of the free portion of the VBA 300. The comb portions of the anchor combs 122C and 132C are supported in the same plane as the mechanical beams 324, 334 and the proof masses 112 and 312, as described above with respect to FIG. 3A and FIG. 1 , respectively.

[0070] FIG. 4Ais a conceptual diagram illustrating a first resonator 420 with additional mass blocks in accordance with one or more techniques of this disclosure. The first resonator 420 can be an example of one or both of the first resonator 120 of FIG. 1A and the first resonator 320 of FIG. 3A. The first resonator 420 can include anchor combs 422A-422C (collectively, “anchor combs 422”), a first mechanical beam 424A, and a second mechanical beam 424 (collectively, “mechanical beams 424”). The first mechanical beam 424A can include additional mass blocks 462A-462D (collectively, “additional mass blocks 462”). The second mechanical beam 424B can include additional mass blocks 464A-464D (collectively, “additional mass blocks 464”). FIG. 1 FIG. 1 The first resonator 420 can include anchor combs 422A-422C (collectively, “anchor combs 422”), a first mechanical beam 424A, and a second mechanical beam 424 (collectively, “mechanical beams 424”). The first mechanical beam 424A can include additional mass blocks 462A-462D (collectively, “additional mass blocks 462”). The second mechanical beam 424B can include additional mass blocks 464A-464D (collectively, “additional mass blocks 464”).

[0071] In some examples, the anchor comb 422A includes one or more anchor comb portions, the anchor comb 422B includes one or more anchor comb portions, and the anchor comb 422C includes one or more anchor comb portions. In some examples, any one or combination of the anchor comb portions of the anchor comb 422A can include one or more electrodes of a first set of electrodes (e.g., the first set of electrodes 128A of FIG. 1A). In some examples, any one or combination of the anchor comb portions of the anchor comb 422B can include one or more electrodes of a second set of electrodes (e.g., the second set of electrodes 128B of FIG. 1A). In some examples, any one or combination of the anchor comb portions of the anchor comb 422C can include one or more electrodes of a third set of electrodes (e.g., the third set of electrodes 128C of FIG. 1A). FIG. 4B

[0072] In some examples, the resonator drive circuit can transmit a drive signal to the first resonator 420 via any one or combination of the first set of electrodes, the second set of electrodes, and the third set of electrodes, thereby causing the first resonator 420 to vibrate at a resonant frequency. For example, the first mechanical beam 424A and the second mechanical beam 424B can vibrate at the resonant frequency described above. In turn, 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 420 can output the first electrical signal, the second electrical signal, and the third electrical signal to the processing circuit (not shown in FIG. 4A), which is configured to determine the resonant frequency of the first resonator 420 based on the first electrical signal, the second electrical signal, and the third electrical signal. FIG. 4A

[0073] In some examples, the resonant frequency of the first resonator 420 can be related to an amount of force applied to the first resonator 420 by a proof mass, such as the proof mass 112 of FIG. 1A. For example, the first end 482 of the first resonator 420 can be fixed to a resonator connection structure (e.g., the resonator connection structure 110 of FIG. 1A). In some examples, the resonant frequency of the first resonator 420 can be related to an amount of force applied to the first resonator 420 by a proof mass, such as the proof mass 112 of FIG. 1A. For example, the first end 482 of the first resonator 420 can be fixed to a resonator connection structure (e.g., the resonator connection structure 110 of FIG. 1A). FIG. 4B FIG. 4B ​​​​and the second end 484 of the first resonator 420 can be fixed to the proof mass. If the proof mass rotates toward the first resonator 420 in response to acceleration in the first direction, the proof mass can exert a compressive force on the first resonator 420. If the proof mass rotates away from the first resonator 420 in response to acceleration in the second direction, the proof mass can exert a tensile force on the first resonator 420. In some examples, if the acceleration is 0 m / s 2 then the proof mass can not exert a force on the first resonator 420. As the compressive force exerted by the proof mass increases in response to an increase in acceleration in the first direction, the resonant frequency of the first resonator 420 can decrease, and as the tensile force exerted by the proof mass increases in response to an increase in acceleration in the second direction, the resonant frequency of the first resonator 420 can increase. In this way, there can be a relationship between the resonant frequency of the first resonator 420 and the acceleration of the accelerometer that includes the first resonator 420.

[0074] The additional masses 462 and 464 can affect the relationship between acceleration and the resonant frequency of the first resonator 420. For example, the quadratic nonlinearity coefficient that defines the relationship between acceleration and the resonant frequency of the first resonator 420 can be smaller than the quadratic nonlinearity coefficient that defines the relationship between acceleration and the resonant frequency of a resonator that does not include the additional masses 462 and 464. It can be advantageous for the relationship between acceleration and the resonant frequency of the first resonator 420 to be as close to linear as possible (e.g., the quadratic nonlinearity coefficient to be as small as possible) in order to ensure that the electrical signals generated by the first resonator 420 allow the processing circuitry to accurately determine the acceleration.

[0075] In some examples, the additional masses 462A and 462B can be placed at a location along the first mechanical beam 424A that is in a range from 25% to 45% of the length of the first mechanical beam 424A along the first end 456 to the second end 457. For example, the additional masses 462A and 462B can be placed at a location that is 35% of the distance between the first end 456 to the second end 457. In some examples, the additional masses 462C and 462D can be placed at a location along the first mechanical beam 424A that is in a range from 55% to 75% of the length of the first mechanical beam 424A along the first end 456 to the second end 457. For example, the additional masses 462C and 462D can be placed at a location that is 65% of the distance between the first end 456 to the second end 457.

[0076] In some examples, additional mass blocks 464A and 464B may be positioned at a location along the second mechanical beam 424B, within a range of 25% to 45% of the length along the second mechanical beam 424B from the first end 458 to the second end 459. For example, additional mass blocks 464A and 464B may be positioned at a location at 35% of the distance between the first end 458 and the second end 459. In some examples, additional mass blocks 464C and 464D may be positioned at a location along the second mechanical beam 424B, within a range of 55% to 75% of the length along the second mechanical beam 424B from the first end 458 to the second end 459. For example, additional mass blocks 464C and 464D may be positioned at a location at 65% of the distance between the first end 458 and the second end 459.

[0077] FIG. 5A This illustrates one or more technologies according to this disclosure, including additional mass blocks 462A and 462B. FIG. 1 to FIG. 2 A conceptual diagram of a portion of the first resonator 420. For example, the first mechanical beam 424A includes a primary component 490 and a set of secondary components 492A to 492D (collectively referred to as the "set of secondary components 492"). FIG. 1 As shown, each of the secondary members in this group of secondary members 492 extends perpendicular to the primary member 490. The first mechanical beam 424A may include FIG. 5A Additional secondary components and other components are not shown. Each secondary component in this group of secondary components 492 may be substantially the same, except that secondary component 492C includes additional mass block 462A and additional mass block 462B.

[0078] FIG. 1 This is a conceptual diagram illustrating a second resonator 530 forming a gap according to one or more techniques of this disclosure. The second resonator 530 can be... FIG. 1 Examples of one or both of the second resonator 130 and the second resonator 330 of FIG. 3A. The second resonator 530 may include anchoring combs 532A to 532C (collectively referred to as "anchoring comb 532"), a third mechanical beam 534A, and a fourth mechanical beam 534B (collectively referred to as "mechanical beam 534"). The third mechanical beam 534A may form gaps 562A to 562D (collectively referred to as "gap 562"). The fourth mechanical beam 534B may form gaps 564A to 564D (collectively referred to as "gap 564").

[0079] In some examples, anchoring comb 532A may include one or more anchoring comb portions, anchoring comb 532B may include one or more anchoring comb portions, and 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 532A may include a fourth set of electrodes (e.g., FIG. 4A to FIG. 4B 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 532B 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 532C may include one or more electrodes of the sixth group of electrodes (e.g., the sixth group of electrodes 138C).

[0080] In some examples, the resonator drive circuit can transmit a drive signal to the second resonator 530 via any one or a combination of the fourth, fifth, and sixth sets of electrodes, causing the second resonator 530 to oscillate at its resonant frequency. For example, the third mechanical beam 534A and the fourth mechanical beam 534B can oscillate at the resonant frequency of the second resonator 530. 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 530 can output the fourth, fifth, and sixth electrical signals to a processing circuit. FIG. 4A to FIG. 4B (Not shown in the image), the processing circuit is configured to determine the resonant frequency of the second resonator 530 based on the fourth, fifth, and sixth electrical signals.

[0081] In some examples, the resonant frequency of the second resonator 530 can be related to that of the test mass block (such as...). FIG. 5B The magnitude of the force applied to the second resonator 530 by the test mass block 112 is related to the magnitude of the force. For example, the first end 582 of the second resonator 530 may be fixed to the test mass block, and the second end 584 of the second resonator 530 may be fixed to the resonator connection structure (e.g., FIG. 5A (Resonator connection structure 116). If the test mass rotates away from the second resonator 530 in response to acceleration in the first direction, the test mass can apply tension to the second resonator 530. If the test mass rotates towards the second resonator 530 in response to acceleration in the second direction, the test mass can apply pressure to the second resonator 530. In some examples, if the acceleration is 0 m / s²... 2The test mass can not apply a force to the second resonator 530. As the test mass applies an increasing pressure in response to an increase in acceleration in the second direction, the resonant frequency of the second resonator 530 can decrease, and as the test mass applies an increasing tension in response to an increase in acceleration in the first direction, the resonant frequency of the second resonator 530 can increase. In this way, there can be a relationship between the resonant frequency of the second resonator 530 and the acceleration of the accelerometer that includes the second resonator 530.

[0082] The gaps 562 and 564 can affect the relationship between acceleration and the resonant frequency of the second resonator 530. For example, the second order nonlinearity coefficient that defines the relationship between acceleration and the resonant frequency of the second resonator 530 can be smaller than the second order nonlinearity coefficient that defines the relationship between acceleration and the resonant frequency of a resonator that does not include the gaps 562 and 564. It can be advantageous for the relationship between acceleration and the resonant frequency of the second resonator 530 to be as close to linear as possible (e.g., the second order nonlinearity coefficient to be as small as possible) in order to ensure that the electrical signals generated by the second resonator 530 allow the processing circuitry to accurately determine the acceleration. In some examples, the gap 562 represents a“hole” and the additional mass 462 is included on the first resonator 420 of the FIG. 5B In some examples, the gap 564 represents a hole and the additional mass 464 is included on the first resonator 420 of the FIG. 5B In some examples, the gap 564 represents a hole and the additional mass 464 is included on the first resonator 420 of the

[0083] In some examples, the gaps 562A and 562B can be placed at a location along the third mechanical beam 534A that is in a range of 25% to 45% of the length of the third mechanical beam 534A from the first end 556 to the second end 557. For example, the gaps 562A and 562B can be placed at a location that is 35% of the distance between the first end 556 and the second end 557. In some examples, the gaps 562C and 562D can be placed at a location along the third mechanical beam 534A that is in a range of 55% to 75% of the length of the third mechanical beam 534A from the first end 556 to the second end 557. For example, the gaps 562C and 562D can be placed at a location that is 65% of the distance between the first end 556 and the second end 557.

[0084] In some examples, gap 564A and gap 564B can be placed at a location along fourth mechanical beam 534B that is in a range from 25% to 45% of a length of fourth mechanical beam 534B along from first end 558 to second end 559. For example, gap 564A and gap 564B can be placed at a location that is 35% of a distance between first end 558 and second end 559. In some examples, gap 564C and gap 564D can be placed at a location along fourth mechanical beam 534B that is in a range from 55% to 75% of a length of fourth mechanical beam 534B along from first end 558 to second end 559. For example, gap 564C and gap 564D can be placed at a location that is 65% of a distance between first end 558 and second end 559.

[0085] FIG. 6 is a conceptual diagram illustrating a portion of a second resonator 530 including gaps 562A and 562B in accordance with one or more techniques of the present disclosure. FIG. 6 For example, third mechanical beam 534A includes a primary member 590 and a set of secondary members 592A-D (collectively, “set of secondary members 592”). As shown in FIG. 7 each secondary member of the set of secondary members 592 extends perpendicular to primary member 590. Third mechanical beam 534A can include additional secondary members and additional other components not shown in FIG. 7 Each secondary member of the set of secondary members 592 can be substantially identical, except that a distance between secondary member 592C and secondary member 592D is greater than a distance between any other pair of consecutive secondary members of the set of secondary members 592.

[0086] FIG. 1 is a graph illustrating a first plot 610 and a second plot 620 in accordance with one or more techniques of the present disclosure, the first plot representing a quadratic nonlinearity coefficient as a function of a location of added mass, and the second plot representing a zero acceleration resonance frequency difference as a function of the location of added mass. For example, “Location of Added Mass” can represent a location of added mass such as added mass 462A and 462B on first mechanical beam 424A, where the location is a percentage of a length of first mechanical beam 424A from first end 456 to second end 457. As shown in FIG. 7As shown in the first plot 610, the second order nonlinearity coefficient (K2) is zero when the position of the additional mass 462A and the additional mass 462B is 35% of the length of the first mechanical beam 424A. Additionally, as seen at point 630 of the second plot 620, the difference between the resonant frequency of the first resonator 420 and the resonant frequency of the second resonator 530 is not zero when the position of the additional mass 462A and the additional mass 462B is 35% of the length of the first mechanical beam 424A. As such, because the second order nonlinearity coefficient is zero and the frequency difference is not zero, the position of the additional mass 462A and the additional mass 462B at 35% of the length of the first mechanical beam 424A can be advantageous.

[0087] In some examples, the point 630 can represent an ideal position of the additional mass 462A and the additional mass 462B along the first mechanical beam 424A. In some examples, the resonant frequency of the first resonator 420 at zero acceleration can be in a range of 25 kilohertz (KHz) to 30 KHz. In some examples, the resonant frequency of the second resonator 530 at zero acceleration can be in a range of 25 kilohertz (KHz) to 30 KHz. In some examples, the difference between the resonant frequency of the first resonator 420 at zero acceleration and the resonant frequency of the second resonator 530 at zero acceleration can be in a range of 250 hertz (Hz) to 3500 Hz when the additional mass 462A and the additional mass 462B are placed at 35% of the length of the first mechanical beam 424A.

[0088] FIG. 2 is a flowchart illustrating example operations for determining an acceleration of a VBA in accordance with one or more techniques of the present disclosure. ​ With respect to ​ The processing circuit 102, the resonator drive circuit 104, and the proof mass assembly 110 are described. However, ​ The techniques of can be performed by different components of the processing circuit 102, the resonator drive circuit 104, and the proof mass assembly 110 or by an additional or alternative accelerometer system.

[0089] The resonator drive circuit 104A can transmit a set of drive signals to the first resonator 120 (702). 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 such that the first resonator 120 vibrates at a resonant frequency. The processing circuit 102 can receive one or more electrical signals indicative of the frequencies of the first mechanical beam 124A and the second mechanical beam 124B via the resonator drive circuit 104A (704). Subsequently, the processing circuit 102 can determine the frequencies of the first mechanical beam 124A and the second mechanical beam 124B based on the one or more electrical signals (706). 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 related to the acceleration of the VBA (such as the VBA 110 of FIG. 1) as described above. As such, the processing circuit 102 can calculate the acceleration of the VBA 110 based on the frequency of the first mechanical beam 124A and the frequency of the second mechanical beam 124B (708). ​

[0090] Although the above example operations are described with respect to the first resonator 120, the processing circuit 102 can additionally or alternatively determine the resonant frequency of the second resonator 130. In some examples, the processing circuit 102 can be configured to determine a difference between the resonant frequency of the first resonator 120 and the resonant frequency of the second resonator 130, and calculate the acceleration based on the difference in resonant frequencies.

[0091] In one or more examples, the accelerometers described herein can implement the described functions using hardware, software, firmware, or any combination thereof. Those functions implemented in software can be stored as one or more instructions or code on a computer-readable medium and executed by a hardware-based processing unit. Computer-readable media can include computer-readable storage media, which corresponds to a tangible medium such as data storage media, or communication media including any medium that facilitates transfer of a computer program from one place to another, e.g., according to a communication protocol. In this manner, computer- readable media generally can correspond to (1) tangible computer-readable storage media which is non-transitory or (2) a communication medium such as a signal or carrier wave. Data storage media can be any available media that can be accessed by one or more computers or one or more processors to retrieve instructions, code and / or data structures for implementation of the techniques described in this disclosure. Examples of a computer- readable storage medium include a hard disk, a CD-ROM, a floppy disk, a magnetic tape, a magnetic

[0092] ​Instructions can be executed or otherwise be communicated by one or more processors within the accelerometer, or that are otherwise communicatively coupled to the accelerometer. These one or more processors can, for example, include one or more DSPs, general purpose microprocessors, application specific integrated circuits (ASICs), FPGAs, or other equivalent integrated or discrete logic circuitry. Accordingly, the term "processor," as used herein can refer to any of the foregoing structure or any other structure suitable for implementation of the techniques described herein. In addition, in some aspects, the functionality described herein can be provided within dedicated hardware and / or software modules configured for performing the techniques described herein. Also, the techniques could be fully implemented in one or more circuits or logic elements.

[0093] The techniques of this disclosure can be implemented in a variety of devices or apparatuses including an integrated circuit (IC) or a set of ICs (e.g., a chip set). Various components, modules, or units described in the disclosure can be implemented as hardware, software, or a combination thereof. Various components, modules, or units described in the disclosure can be implemented as software and / or firmware configured to be executed by one or more processors electrically coupled to an IC and / or an array of ICs. Various components, modules, or units described in the disclosure can be implemented in hardware and / or software (e.g., as a set of instructions executable by one or more processors). These various components, modules, or units often intercommunicate using well-known computer processing techniques and protocols. The techniques of this disclosure can be implemented in various apparatuses or devices that include an integrated circuit (IC) or a set of ICs (e.g., a chip set). Various components, modules, or units described in the disclosure can be implemented as hardware, software, or a combination thereof. Various components, modules, or units described in the disclosure can be implemented as software and / or firmware configured to be executed by one or more processors electrically coupled to an IC and / or an array of ICs. Various components, modules, or units described in the disclosure can be implemented in hardware and / or software (e.g., as a set of instructions executable by one or more processors). These various components, modules, or units often intercommunicate using well-known computer processing techniques and protocols.

Claims

1. An accelerometer system comprising: a proof mass assembly comprising: a proof mass; a resonator connection structure, wherein the resonator connection structure extends parallel to a long axis; a hinge flexure configured to connect the proof mass to the resonator connection structure, wherein the proof mass rotates about the hinge flexure in response to acceleration of the system parallel to the long axis of the resonator connection structure; and a first resonator configured to connect the proof mass to the resonator connection structure, wherein the first resonator comprises: a first mechanical beam comprising a first primary member extending parallel to the long axis and a first secondary member perpendicular to the first primary member, wherein the first mechanical beam comprises a first additional mass located at a point along the long axis, and wherein the first additional mass is connected to the first secondary member; and a second mechanical beam comprising a second primary member extending parallel to the long axis and a second secondary member perpendicular to the second primary member, wherein the second mechanical beam comprises a second additional mass located at the point along the long axis, and wherein the second additional mass is connected to the second secondary member; and processing circuitry configured to: receive one or more electrical signals from the first resonator indicative of a frequency of the first mechanical beam and a frequency of the second mechanical beam; determine the frequency of the first mechanical beam and the frequency of the second mechanical beam based on the one or more electrical signals; and calculate an acceleration of the proof mass assembly based on the frequency of the first mechanical beam and the frequency of the second mechanical beam.

2. The system of claim 1, wherein the first mechanical beam comprises a set of first secondary members, wherein each first secondary member of the set of first secondary members extends perpendicular to the long axis, wherein the set of first secondary members comprises a first secondary member connected to the first additional mass, and wherein the second mechanical beam comprises a set of second secondary members, wherein each second secondary member of the set of second secondary members extends perpendicular to the long axis, and wherein the set of second secondary members comprises a second secondary member connected to the second additional mass.

3. The system of claim 1, wherein the one or more electrical signals comprise a first one or more electrical signals, wherein the point along the long axis of the resonator connection structure axis comprises a first point along the long axis, and wherein the proof mass assembly further comprises: a second resonator configured to connect the proof mass to the resonator connection structure, wherein the second resonator comprises: a third mechanical beam extending parallel to the long axis of the resonator connection structure, wherein the third mechanical beam forms a first gap located at a second point along the long axis; and a fourth mechanical beam extending parallel to the long axis of the resonator connection structure, wherein the fourth mechanical beam forms a second gap located at the second point along the long axis. a fourth mechanical beam extending parallel to the long axis, wherein the fourth mechanical beam forms a second gap located at the second point along the long axis, and wherein the processing circuit is further configured to: receive, from the second resonator, a second one or more electrical signals indicative of a frequency of the third mechanical beam and a frequency of the fourth mechanical beam; determine the frequency of the third mechanical beam and the frequency of the fourth mechanical beam based on the second one or more electrical signals; and calculate the acceleration of the proof mass assembly based on the frequency of the third mechanical beam and the frequency of the fourth mechanical beam.

4. The system of claim 3, wherein the third mechanical beam comprises: a third primary member extending parallel to the long axis of the resonator connection structure; and a set of third secondary members, wherein each third secondary member of the set of third secondary members extends perpendicular to the long axis, wherein at least one third secondary member of the set of third secondary members forms the first gap, and wherein the fourth mechanical beam comprises: a fourth primary member extending parallel to the long axis; and a set of fourth secondary members, wherein each fourth secondary member of the set of fourth secondary members extends perpendicular to the long axis, and wherein at least one fourth secondary member of the set of fourth secondary members forms the second gap.

5. The system of claim 3, wherein the proof mass assembly further comprises: a first set of electrodes placed on an exterior of the first resonator adjacent to the first mechanical beam, wherein the first set of electrodes is configured to generate a first electrical signal of the first one or more electrical signals; a second set of electrodes placed between the first mechanical beam and the second mechanical beam, wherein the second set of electrodes is configured to generate a second electrical signal of the first one or more electrical signals; and a third set of electrodes placed on an exterior of the first resonator adjacent to the second mechanical beam, wherein the third set of electrodes is configured to generate a third electrical signal of the first one or more electrical signals, and wherein to determine the frequency of the first mechanical beam and the frequency of the second mechanical beam, the processing circuit is configured to: calculate a difference between the first electrical signal and the second electrical signal; calculate a difference between the second electrical signal and the third electrical signal; calculate the frequency of the first mechanical beam based on the difference between the first electrical signal and the second electrical signal; and calculate the frequency of the second mechanical beam based on the difference between the second electrical signal and the third electrical signal.

6. The system of claim 5, wherein the proof mass assembly further comprises: a fourth set of electrodes placed on an exterior of the second resonator adjacent to the third mechanical beam, wherein the fourth set of electrodes is configured to generate a fourth electrical signal of the second one or more electrical signals; a fifth set of electrodes positioned between the third mechanical beam and the fourth mechanical beam, wherein the fifth set of electrodes is configured to generate a fifth electrical signal of the second one or more electrical signals; and a sixth set of electrodes positioned on an exterior of the second resonator proximate to the fourth mechanical beam, wherein the sixth set of electrodes is configured to generate a sixth electrical signal of the second one or more electrical signals, and wherein to determine the frequency of the third mechanical beam and the frequency of the fourth mechanical beam, the processing circuit is configured to: calculate a difference between the fourth electrical signal and the fifth electrical signal; calculate a difference between the fifth electrical signal and the sixth electrical signal; calculate the frequency of the third mechanical beam based on the difference between the fourth electrical signal and the fifth electrical signal; and calculate the frequency of the fourth mechanical beam based on the difference between the fifth electrical signal and the sixth electrical signal.

7. The system of claim 6, wherein the processing circuit is further configured to: determine a frequency of the first resonator based on the frequency of the first mechanical beam and the frequency of the second mechanical beam; determine a frequency of the second resonator based on the frequency of the third mechanical beam and the frequency of the fourth mechanical beam; calculate a difference between the frequency of the first resonator and the frequency of the second resonator; and calculate the acceleration of the proof mass assembly based on the difference between the frequency of the first resonator and the frequency of the second resonator.

9. The system of claim 1, wherein the first mechanical beam includes a first proximal end and a first distal end, and wherein the point of the first additional mass along the long axis of the resonator connection structure is located in a range of 0.25 to 0.45 of a length of the first mechanical beam from the first proximal end to the first distal end.

8. The system of claim 7, wherein the difference between the frequency of the first resonator and the frequency of the second resonator is greater than zero in magnitude when the acceleration of the proof mass assembly is zero meters per second squared (m / s 2 ).

10. A method for determining an acceleration of a seismic beam accelerometer, the method comprising: receiving, by processing circuitry, one or more electrical signals indicative of a frequency of a first mechanical beam and a frequency of a second mechanical beam from a first resonator, wherein a proof mass assembly includes: a proof mass; a resonator connection structure, wherein the resonator connection structure extends parallel to a long axis; a hinge flexure configured to connect the proof mass to the resonator connection structure, wherein the proof mass rotates about the hinge flexure in response to an acceleration of the accelerometer parallel to the long axis of the resonator connection structure; and the first resonator configured to connect the proof mass to the resonator connection structure, wherein the first resonator includes: the first mechanical beam including a first primary member extending parallel to the long axis and a first secondary member perpendicular to the first primary member, wherein the first mechanical beam includes a first additional mass located at a point along the long axis, and wherein first additional mass is connected to the first secondary member; and the first resonator configured to connect the proof mass to the resonator connection structure, wherein the first resonator includes: the first mechanical beam including a first primary member extending parallel to the long axis and a first secondary member perpendicular to the first primary member, wherein the first mechanical beam includes a first additional mass located at a point along the long axis, and wherein first additional mass is connected to the first secondary member; and the second mechanical beam includes a second primary member extending parallel to the long axis and a second secondary member perpendicular to the second primary member, wherein the second mechanical beam includes a second additional mass located at the point along the long axis, and wherein the second additional mass is connected to the second secondary member; determining, by the processing circuit and based on the one or more electrical signals, the frequency of the first mechanical beam and the frequency of the second mechanical beam; and calculating, by the processing circuit and based on the frequency of the first mechanical beam and the frequency of the second mechanical beam, an acceleration of the proof mass assembly.

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