A Tuning Fork Gyroscope with a Polygon-Shaped Vibration Beam

micromachines

Article A Tuning Fork Gyroscope with a Polygon-Shaped Vibration Beam

Qiang Xu, Zhanqiang Hou *, Yunbin Kuang, Tongqiao Miao, Fenlan Ou, Ming Zhuo, Dingbang Xiao and Xuezhong Wu *

College of Intelligence Science and Engineering, National University of Defense Technology, Changsha 410073, China; [email protected] (Q.X.); [email protected] (Y.K.); [email protected] (T.M.); [email protected] (F.O.); [email protected] (M.Z.); [email protected] (D.X.) * Correspondence: [email protected] (Z.H.); [email protected] (X.W.)

Received: 22 October 2019; Accepted: 18 November 2019; Published: 25 November 2019

Abstract: In this paper, a tuning fork gyroscope with a polygon-shaped vibration beam is proposed. The vibration structure of the gyroscope consists of a polygon-shaped vibration beam, two supporting beams, and four vibration masts. The spindle azimuth of the vibration beam is critical for performance improvement. As the spindle azimuth increases, the proposed vibration structure generates more driving amplitude and reduces the initial capacitance gap, so as to improve the signal-to-noise ratio (SNR) of the gyroscope. However, after taking the driving amplitude and the driving voltage into consideration comprehensively, the optimized spindle azimuth of the vibration beam is designed in an appropriate range. Then, both wet etching and dry etching processes are applied to its manufacture. After that, the fabricated gyroscope is packaged in a vacuum ceramic tube after bonding. Combining automatic gain control and weak capacitance detection technology, the closed-loop control circuit of the drive mode is implemented, and high precision output circuit is achieved for the gyroscope. Finally, the proposed Micro Electro Mechanical Systems (MEMS) gyroscope system demonstrates a bias instability of 0.589◦/h, an angular random walk (ARW) of 0.038◦/√h, and a bandwidth of greater than 100 Hz in a full scale range of 200 /s at room temperature. ± ◦ Keywords: tuning fork gyroscope; spindle azimuth; vibration beam; bias instability; angular random walk

1. Introduction The Micro Electro Mechanical Systems (MEMS) gyroscope has had great importance in all countries over the past 20 years due to its small size, low cost, low power consumption, and batch fabrication. Micromachined gyroscopes have been widely used in the fields of electronics consumer goods, vehicle safety, weaponry, and other fields [1–3]. A significant amount of research has been carried out on the different kinds of micromachined gyroscopes over the past decades, which has directly promoted the development of high performance gyroscopes for various applications. Among the different kinds of MEMS gyroscopes, the typical structures include turning forks (TFG) [4–8], combs [9–11], rings or disks [12–15], or micro wineglass [16–18]. The most common type of MEMS gyroscope design is the TFG, a shuttling proof mass design that can be operated in either mode-matched or mode-split conditions. Matched mode tuning fork gyroscopes achieved near navigation-grade performance in [19], where values of 0.003◦/√h angular random walk (ARW) and 0.16◦/h bias instability were reported. However, its bandwidth was only 1 Hz, failing most navigation application requirements (usually larger than 100 Hz). On the contrary, a gyroscope working in split mode will have a wider bandwidth, but the mechanical sensitivity is not high. So far, there is no split mode gyroscope that can be compared with the performance of a

Micromachines 2019, 10, 813; doi:10.3390/mi10120813 www.mdpi.com/journal/micromachines Micromachines 2019, 10, 813 2 of 17 mode-matched gyroscope. In summary, split mode tuning fork micromachined gyroscopes that can meet the requirements of inertial level are rarely reported. Therefore, enhancing the sensitivity is important for split mode tuning fork gyroscopes. The application field for gyroscopes is determined by their sensitivity; only those gyroscopes with high sensitivity can be applied in the fields requiring small variation in angular velocity. Additionally, the signal-to-noise ratio (SNR) of the gyroscope system will increase after the sensitivity is improved. When the same intensity signal is output by the system, the overall noise of the system is relatively reduced. It is known that greater driving amplitude and larger initial capacities can lead to higher SNR as well as sensitivity. However, if the driving amplitude is too large, the vertical component displacements will be so great that the vibration mass will collide with the glass substrate. Therefore, the gap between the vibration structure and glass (initial capacitive gap) must be larger to avoid the collision. However, this larger gap could result in low sensitivity due to the smaller initial capacity. Therefore, the vertical component of driving displacement becomes one of key factors limiting the sensitivity of tuning fork gyroscopes. In order to reduce the restriction, the vertical component of the driving displacement must be decreased. However, the vertical component of the driving displacement is related to the spindle azimuth of the vibration beam. Therefore, reasonable design of the cross-section of the vibration beam could improve the spindle azimuth, so as to enhance the sensitivity of the tuning fork gyroscope. The vibration beam of the micromachined tuning fork gyroscope in our research group is a parallelogram beam, which is fabricated by wet etching [20,21]. Driven by the vertical driving force, the vibration structure generates both horizontal and vertical displacements caused by the parallelogram vibration beam. As there is no structure with a high aspect ratio, this kind of gyroscope structure can be fabricated only by anisotropic wet etching process on a single crystal silicon chip, without advanced dry etching process equipment [22,23]. The processing technology is simple and the cost is low due to the low price of the materials used. However, the spindle azimuth of the parallelogram beam is no larger than 54.74◦. Therefore, the sensitivity of the gyroscope is low due to the small spindle azimuth being limited by wet etching process. A novel silicon bulk gyroscope was proposed by the Sensonor company [24–26]. The overall size of the gyroscope structure is very small, benefiting from the unique processing technology, which combines the dry and wet etching. The cross-section of the vibration beam is an irregular polygon, whose spindle azimuth was designed by changing the processing parameters, so the sensitivity of the gyroscope was enhanced by increasing the spindle azimuth. However, as for the dry etching process, it has a strong dependence on advanced processing equipment, and small structure processing requires Silicon-On-Insulator (SOI) chips, which makes the fabrication process more complex and costly than for single crystal silicon chips. A vibration beam adopting a polygonal cross-section was proposed in order to enhance sensitivity and robustness [27]. Comparison between the proposed polygonal vibration beam and the convex vibration beam on the tolerance capacity analysis was carried out. After comparison, the conclusion was made that the polygonal oblique beam had better tolerance for fabrication imperfections than the convex oblique beam. Taking all the different kinds of MEMS gyroscopes mentioned above into consideration, in this paper, a tuning fork gyroscope with a polygon-shaped vibration beam is presented. Based on a single crystal silicon chip, the structure is manufactured using processing technology that combines dry and wet etching. Therefore, the following benefits can be obtained:

1. The spindle azimuth can be increased by designing the cross-section of the vibration beam. Therefore, the proposed structure with the optimized vibration beam not only increases the driving amplitude, but also reduces the initial capacitance gap in the sensing direction, so as to enhance the signal-to-noise ratio (SNR) as well as the sensitivity of the gyroscope. Micromachines 2019, 10, x 3 of 17 Micromachines 2019, 10, x 3 of 17 Micromachines 2019, 10, 813 3 of 17 2. The polygonal vibration beam fabricated by the wet and dry etching is much more stable 2. The polygonal vibration beam fabricated by the wet and dry etching is much more stable and much more insensitive to the fabrication imperfections, which provides the tuning and much more insensitive to the fabrication imperfections, which provides the tuning 2. Thefork polygonal gyroscope vibration with good beam ro fabricatedbustness and by the repeatability. wet and dry etching is much more stable and fork gyroscope with good robustness and repeatability. 3.much The more use insensitive of single crystal to the fabricationsilicon chips imperfections, instead of SOI which chips provides reduces the the tuning complexity fork gyroscope and cost 3. The use of single crystal silicon chips instead of SOI chips reduces the complexity and cost withof good the fabrication robustness process. and repeatability. 3. The useof the of fabrication single crystal process. silicon chips instead of SOI chips reduces the complexity and cost of the 2. Materialsfabrication and process.Methods Design for the Proposed Gyroscope 2. Materials and Methods Design for the Proposed Gyroscope The main idea of the design of the vibration structure is to optimize the cross-section of the 2. MaterialsThe main and idea Methods of the Designdesign of for the the vibration Proposed structure Gyroscope is to optimize the cross-section of the vibration beam by improving the spindle azimuth, which should reduce the vertical driving vibration beam by improving the spindle azimuth, which should reduce the vertical driving amplitudeThe main and ideaenlarge of the the design driving of amplitude, the vibration so structureas to enhance is to optimizethe SNR theand cross-section sensitivity of of the amplitude and enlarge the driving amplitude, so as to enhance the SNR and sensitivity of the gyroscope.vibration beam by improving the spindle azimuth, which should reduce the vertical driving amplitude gyroscope.and enlarge the driving amplitude, so as to enhance the SNR and sensitivity of the gyroscope. 2.1. Overall Design of the Proposed Gyroscope 2.1. Overall Design of the Proposed Gyroscope The conventional tuning fork micromachined gyroscope in our work is manufactured by wet The conventional tuning fork micromachined gyr gyroscopeoscope in in our work is manufactured by wet etching, and the cross-section of the vibration beam is a parallelogram whose spindle azimuth (θp) is etching, and the cross-section of the vibration beam is aa parallelogramparallelogram whosewhose spindlespindle azimuthazimuth ((θθp) is no larger than 54.74°, as shown in Figure 1. p no larger than 54.74°, 54.74◦, as as shown shown in in Figure Figure 1.1.

(a) (b) (a) (b)

FigureFigure 1. 1.Conventional Conventional tuning tuning forkfork micromachinedmicromachined gyroscope. (a (a) )The The structure structure model. model. (b) ( bThe) The Figure 1. Conventional tuning fork micromachined gyroscope. (a) The structure model. (b) The structural parameters. structural parameters. structural parameters.

Here, O is the rotation center of the driving mode,mode, wdd is the width of driving electrode, wb isis the the Here, O is the rotation center of the driving mode, wd is the width of driving electrode, wb is the distance between two driving electrodes, ll11 isis distance distance between between vibration vibration beam beam and and vibration vibration mass, mass, distance between two driving electrodes, l1 is distance between vibration beam and vibration mass, and l2 isis the the length length of of the the vibration vibration mass. mass. and l2 is the length of the vibration mass. When excited in the driving mode, the vibration mass can generate both horizontal and vertical When excited in the driving mode, the vibration mass can generate both horizontal and vertical displacements, as as shown in Figure 22.. DriveXDriveX isis the the horizontal horizontal component component of of driving driving displacement, displacement, displacements, as shown in Figure 2. DriveX is the horizontal component of driving displacement, DriveZ is the vertical component of driving displacement, andand dd isis thethe initialinitial capacitancecapacitance gapgap ((dd).). DriveZ is the vertical component of driving displacement, and d is the initial capacitance gap (d).

mass θ mass θp DriveX

o p DriveX

D θp

d v i

d v Z e

electrodeZ electrode electrode electrode

Figure 2. Vertical and horizontal component of driving displacement. Figure 2. Vertical and horizontal component of driving displacement. Figure 2. Vertical and horizontal component of driving displacement. According to Figure2, DriveX and DriveZ can be described as: According to Figure 2, DriveX and DriveZ can be described as: According to Figure 2, DriveX and DriveZ can be described as:  = ( ) ( + )  DriveX φd sin θp l1 l2 /2  · · (1)  DriveZ = φ cos(θp) (w + w )/2 d · · d b

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DriveX=⋅φθsin( ) ⋅+ ( l l ) / 2  DriveX=⋅φθdpsin( ) ⋅+ (12 l l ) / 2  dp12 (1) Micromachines 2019, 10, 813 DriveZ=⋅φθcos( ) ⋅ ( w + w ) / 2 4 of(1) 17  DriveZ=⋅φθdpdbcos( ) ⋅ ( w + w ) / 2  dpdb The maximum vertical component of driving displacement (MaxdriveZ) is d/3, due to the pull-in The maximum vertical component of driving displacement (MaxdriveZ) is d/3, due to the pull-in effect.The Therefore, maximum the vertical maximum component horizontal of drivingcomponent displacement of the driving (MaxdriveZ displacement) is d/3, due(MaxdriveX to the pull-in) can effect. Therefore, the maximum horizontal component of the driving displacement (MaxdriveX) can beeﬀ ect.described Therefore, as: the maximum horizontal component of the driving displacement (MaxdriveX) can be be described as: described as: MaxdriveX=⋅(/3)tan()( dθ ⋅++ l l )/( w w ) =⋅θp ⋅++12 db (2) MaxdriveXMaxdriveX= (d/(/3)tan()(3 d) tan(θpp) ( ll12+ l )/(l )/ w(dbw w+ )w ) (2)(2) · · 1 2 d b From Equation (2), we can see that if the other parameters are constant, MaxdriveX will become FromFrom EquationEquation (2),(2), wewe cancan seesee thatthat ifif thethe otherother parametersparameters areare constant,constant, MaxdriveXMaxdriveX willwill becomebecome larger as the θp grows larger. largerlarger asas thethe θθpp grows larger. In order to enlarge the driving amplitude and enhance the SNR, the cross-section of the InIn orderorder to to enlarge enlarge the the driving driving amplitude amplitude and enhanceand enhance the SNR, the the SNR, cross-section the cross-section of the vibration of the vibration beam is designed to increase the spindle azimuth. The proposed structure is fabricated by beamvibration is designed beam is to designed increase theto increase spindle azimuth.the spindle The azimuth. proposed The structure proposed is fabricated structure byis fabricated both wet and by both wet and dry etching, as shown in Figure 3. The cross-section is an irregular polygon whose dryboth etching, wet and as dry shown etching, in Figure as shown3. The in cross-section Figure 3. The is an cross-section irregular polygon is an irregular whose spindle polygon azimuth whose spindle azimuth could be designed by changing processing parameters. couldspindle be azimuth designed could by changing be designed processing by changing parameters. processing parameters.

Figure 3. Proposed gyroscope with optimized vibration beam. FigureFigure 3.3. Proposed gyroscope withwith optimizedoptimized vibrationvibration beam.beam. 2.2.2.2. Impact Impact Factors Factors of of the the Spindle Spindle Azimuth Azimuth 2.2. Impact Factors of the Spindle Azimuth TheThe spindle spindle azimuth azimuth of of the the vibration vibration beam beam is is re relatedlated to to the driving amplitude, and and it it can can be be The spindle azimuth of the vibration beam is related to the driving amplitude, and it can be increasedincreased by by optimizing optimizing the the cross-se cross-sectionction shape of the vibration beam. increased by optimizing the cross-section shape of the vibration beam. AccordingAccording to to Equation Equation (2), (2), the the MaxdriveXMaxdriveX isis plotted plotted under under different diﬀerent gaps ( d).). As As can can be be seen seen in in According to Equation (2), the MaxdriveX is plotted under different gaps (d). As can be seen in FigureFigure 44,, thethe MaxdriveXMaxdriveXgrows grows with with the the increase increase of ofθ pθandp and gap gap (d ).(d The). The closer closerθp θisp tois 90to◦ 90°,, the the faster faster the Figure 4, the MaxdriveX grows with the increase of θp and gap (d). The closer θp is to 90°, the faster theMaxdriveX MaxdriveXincreases, increases, especially especially when whenθp is greaterθp is greater than 80than◦. Therefore, 80°. Therefore, in order in toorder improve to improve the driving the the MaxdriveX increases, especially when θp is greater than 80°. Therefore, in order to improve the drivingamplitude amplitude and enhance and enhance the SNR, the a largerSNR, aθ plargershould θp beshould chosen be inchosen the following in the following design. design. driving amplitude and enhance the SNR, a larger θp should be chosen in the following design.

Figure 4. The maximum horizontal component of of the the driving driving displacement displacement ( (MaxdriveXMaxdriveX)) varies varies with with Figure 4. The maximum horizontal component of the driving displacement (MaxdriveX) varies with the spindle azimuth (θthep) and spindle initial azimuth capacitance (θp) and gap initial (d). capacitance gap (d). the spindle azimuth (θp) and initial capacitance gap (d). As the spindle azimuth (θ ) and initial gap (d) grow, the MaxdriveX will be enhanced. However, As the spindle azimuth (θpp) and initial gap (d) grow, the MaxdriveX will be enhanced. However, As the spindle azimuth (θp) and initial gap (d) grow, the MaxdriveX will be enhanced. However, thethe driving driving voltage voltage required required to to drive drive the the vibration vibration mass mass will will be be much much higher, higher, resulting resulting from from the the the driving voltage required to drive the vibration mass will be much higher, resulting from the mechanicalmechanical characteristics of vibration beams with a large spindle azimuth. mechanical characteristics of vibration beams with a large spindle azimuth.

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MicromachinesMicromachines 2019 2019, ,10 10, ,x x 55 of of 17 17 According to the research our previous research, the AC voltage (V ), which is required to drive According to the research our previous research, the AC voltage (Vacac), which is required to drive According to the research our previous research, the AC voltage (Vac), which is required to drive the vibration mass to d/3 in the vertical displacement, can be described as [27]: thethe vibrationvibration massmass toto dd/3/3 inin thethe verticalvertical displacement,displacement, cancan bebe describeddescribed asas [27]:[27]: 23 232 3 IIwdddw d 2 = Iwdd d 2 θ Vac= dd sec (θ2 p ) (3) VacVac= ε secsec ( p( )θp) (3)(3) 3ε lXAVQydddcd 33εllXAVQyydddcdXdAdVdcQd

where Id is the moment of inertia of the driving axis, ωd is the frequency of the driving mode, d is the wherewhere IIdd isis the the moment moment of of inertia inertia of of the the driving driving axis, axis, ωωdd isis the the frequency frequency of of the the driving driving mode, mode, dd isis the the initialinitialinitial capacitor capacitorcapacitor gap gap between between the the silicon silicon st structurestructureructure and and the the glass glass electrode electrodeelectrode substrate, substrate, εε isisis the thethe electric electricelectric constant, ly is the distance from the rotation center to the far end of the mass, Xd is the half distance of constant,constant, llyy isis the the distance distance from from the the rotation rotation center center to to the the far far end end of ofthe the mass, mass, XdX isd theis the half half distance distance of the two adjacent driving capacitor centers, Ad is the area of the driving electrodes, Vdc is the DC theof thetwo two adjacent adjacent driving driving capacitor capacitor centers, centers, AdA isd isthe the area area of of the the driving driving electrodes, electrodes, Vdcdc isis the the DCDC voltage required to drive the structure, and Qd is the quality factor of the driving mode. voltagevoltage required required to drive the structure, and Qd isis the the quality quality factor factor of of the the driving driving mode. mode. According to Equation (3), when the other parameters are constant, the relationship between Vac AccordingAccording to to Equation Equation (3), (3), when when the other para parametersmeters are constant, the relationship between Vac and θp is as shown in Figure 5. As can be seen from the curve, when θp is greater than 80°, the andandθp isθp as is shownas shown in Figure in Figure5. As 5. can As becan seen be seen from from the curve, the curve, when whenθp is θ greaterp is greater than than 80◦, the80°, required the required driving AC voltage (Vac) grows quickly, which is difficult when designing a high-voltage drivingrequiredAC drivingvoltage AC (V voltageac) grows (V quickly,ac) grows which quickly, is di whichﬃcult is when difficul designingt when designing a high-voltage a high-voltage circuit. circuit.circuit.

Figure 5. The required AC driving voltage (Vac) varies with the spindle azimuth. Figure 5. The required AC driving voltage (Vac) varies with the spindle azimuth. Figure 5. The required AC driving voltage (Vac) varies with the spindle azimuth.

In thethe designdesign of of the the spindle spindle azimuth azimuth (θp ),(θ bothp), both the highthe high sensitivity sensitivity and low and driving low driving voltage voltage should In the design of the spindle azimuth (θp), both the high sensitivity and low driving voltage shouldbeshould taken bebe into takentaken consideration. intointo consideration.consideration. 2.3. Calculation of the Spindle Azimuth 2.3.2.3. CalculationCalculation ofof thethe SpindleSpindle AzimuthAzimuth The key dimensions of the cross-section of the proposed vibration beam are shown in Figure6. TheThe keykey dimensionsdimensions ofof thethe cross-sectioncross-section ofof thethe prproposedoposed vibrationvibration beambeam areare shownshown inin FigureFigure 6.6.

FigureFigure 6. 6. The The key key dimensions dimensions of of the the cross-sect cross-sect cross-sectionionion of of the the proposed proposed vibration vibration beam. beam.

FromFrom FigureFigure 6,6, itit cancan bebe seenseen thatthat wetwet etchingetching isis carriedcarried outout onon thethe basisbasis ofof aa largelarge rectangle,rectangle, andand the right-angled trapezoid part is fabricated by wet etching. Here, Oc is the centroid of the irregular the right-angled trapezoid part is fabricated by wet etching. Here, Oc is the centroid of the irregular

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From Figure6, it can be seen that wet etching is carried out on the basis of a large rectangle, Micromachinesand the right-angled 2019, 10, x trapezoid part is fabricated by wet etching. Here, Oc is the centroid of the irregular6 of 17 polygon, and O2 is the centroid of the right-angle trapezoid, which consists a right triangle (As) and a polygon,small rectangle and O2 is( theAj). centroid of the right-angle trapezoid, which consists a right triangle (As) and a small rectangleTherefore, (Aj the). spindle azimuth of the proposed vibration beam can be accurately controlled by changingTherefore, the the width spindle (w) and azimuth depth of (h )the of wetproposed etching. vibration beam can be accurately controlled by changing the width (w) and depth (h) of wet etching. In order to design the spindle azimuth of the irregular polygon (θp), the moments of inertia (I_xc In order to design the spindle azimuth of the irregular polygon (θp), the moments of inertia (I_xc and I_yc) and the product of inertia (I_xcyc) of the irregular polygon should be calculated beforehand, andafter I_yc which) and the the product spindle of azimuth inertia can(I_x becyc) calculated of the irregular and described polygon should as [28]: be calculated beforehand, after which the spindle azimuth can be calculated and described as [28]: angle ===−⋅angle = 90 arctan[2 I_xc yc/(I_ −yc I_xc)]/ ⋅⋅=π(2 π 180) = f (w, h) (4) angle angle90− arctan[2 I· xcc y / ( I y c I− x c )] / (2 180)· · f ( w , h ) (4)

AccordingAccording to Equation to Equation (4), (4), we we can can see see that that the the spindle spindle azimuth azimuth of ofthe the irregular irregular polygon polygon (θp ()θ isp) is affectedaﬀected by bythe the width width (w ()w and) and depth depth (h) ( hof) ofwet wet etching, etching, as asshown shown in inFigure Figure 7.7 .

Figure 7. The spindle azimuth (θp) varies with the width (w) and depth (h) of wet etching. Figure 7. The spindle azimuth (θp) varies with the width (w) and depth (h) of wet etching. 2.4. Design of the Main Dimensions of the Cross-Section 2.4. Design of the Main Dimensions of the Cross-Section According to Figure7, when the other conditions are constant, the spindle azimuth ( θp) decrease asAccording the depth ( hto) of Figure wet etching 7, when deepens, the other and the cond spindleitions azimuth are constant, (θp) decreases the spindle first and azimuth then increases (θp) decreaseas the widthas the (wdepth) becomes (h) of wider. wet etching Therefore, deepens, when and designing the spindle the spindle azimuth azimuth (θp) decreases (θp), the zone first aroundand thenthe increases minimum as pointthe width on the (w) curve becomes is a betterwider. choiceTherefore, due towhen the designing insensitivity the to spindle dimensional azimuth errors (θp), of thewidth zone (waround). the minimum point on the curve is a better choice due to the insensitivity to dimensionalWhen errors the width of width (w) becomes(w). larger, the curves with different etching depths (h) become closer. ThatWhen is to the say, width the spindle (w) becomes azimuth larger, (θp )the is insensitivecurves with to different dimensional etching errors depths of wet (h) become etching depthcloser. (h) Thatwhen is to the say, width the spindle of wet etching azimuth (w ()θ becomesp) is insensitive larger. to dimensional errors of wet etching depth (h) when theIn width order toof obtainwet etching a better (w) spindlebecomes azimuth larger. (θp) that is less affected by fabrication errors, both theIn width order errorto obtain and a depth better error spindle should azimuth be considered (θp) that is comprehensively. less affected by fabrication The different errors, processing both theparameters width error for and the depth spindle error azimuth should are be calculated considered with comprehensively. the same processing The errors. different processing parametersAfter for comparison the spindle betweenazimuth theare calculated different approaches, with the same the processing optimized errors. combination of structure parametersAfter comparison is obtained, between providing the insensitivitydifferent approa to dimensionalches, the optimized errors. As cancombination be seen in of Figure structure8, point parametersA is the idealis obtained, design ofproviding the spindle insensitivity azimuth onto thedimensional second line, errors. and As the can other be fourseen pointsin Figure (B, C,8, D, pointand A E) is arethe the ideal results design with of 1theµm spindle error inazimuth depth andon the 2 µ secondm error line, in width. and the other four points (B, C, D, and E) are the results with 1 μm error in depth and 2 μm error in width.

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Figure 8. The spindle azimuth (θp) varies with the processing errors. Figure 8. Figure 8. TheThe spindle spindle azimuth azimuth (θ (θp)p )varies varies with with the the processing processing errors.errors. The optimized structural parameters of the proposed vibration structure are determined by The optimized structural parameters of the proposed vibration structure are determined by theoreticalThe optimized analysis, structuralfinite element parameters simulation, of the andproposed experimental vibration verification. structure are Using determined the finite by theoretical analysis, finite element simulation, and experimental verification. Using the finite element elementtheoretical analysis analysis, method, finite the element modal simulationsimulation, analys and isexperimental of the tuning verification. fork gyroscope Using is carried the finite out analysis method, the modal simulation analysis of the tuning fork gyroscope is carried out in the inelement the simulation analysis method,software theCOMSOL modal simulationMultiphysics, analys andis the of simulationthe tuning forkmotion gyroscope form of isthe carried working out simulation software COMSOL Multiphysics, and the simulation motion form of the working mode of modein the ofsimulation the gyroscope software can beCOMSOL obtained. Multiphysics, The simulation and results the simulation for drive motionand sense form modes of the are working shown the gyroscope can be obtained. The simulation results for drive and sense modes are shown in Figure9. inmode Figure of the9. gyroscope can be obtained. The simulation results for drive and sense modes are shown in Figure 9.

(a) (b) (a) (b) Figure 9. The modal simulation results: (a) drive mode (3253.8 Hz); (b) sense mode (3414.7 Hz). Figure 9. The modal simulation results: (a) drive mode (3253.8 Hz); (b) sense mode (3414.7 Hz). Figure 9. The modal simulation results: (a) drive mode (3253.8 Hz); (b) sense mode (3414.7 Hz). As can be seen from Figure9, the drive mode shown in Figure9a is the bending motion of the As can be seen from Figure 9, the drive mode shown in Figure 9a is the bending motion of the vibration beam. The sense mode shown in Figure9b is the torsional motion of the vibration beam. vibrationAs can beam. be seen The sensefrom Figuremode shown9, the drive in Figure mode 9b shown is the torsionalin Figure motion 9a is the of bendingthe vibration motion beam. of the 2.4.1.vibration Driving beam. Mode The sense mode shown in Figure 9b is the torsional motion of the vibration beam. 2.4.1. Driving Mode 2.4.1.There Driving are Mode a pair of diﬀerential drive electrodes and a detection electrode under each vibration massThere block, are as showna pair of in Figuredifferential3. When drive driving electrodes voltages and are a detection applied to electrode the di ﬀerential under driveeach vibration electrode There are a pair of differential drive electrodes and a detection electrode under each vibration plates,mass block, the driving as shown electrostatic in Figure force 3. When will be driving generated. voltages When are excited applied by to the the driving differential electrostatic drive mass block, as shown in Figure 3. When driving voltages are applied to the differential drive electrodeforce, bending plates, deformation the driving occurs electrostatic in the vibrationforce will beam, be generated. so the vibration When massexcited block by oscillatesthe driving in electrode plates, the driving electrostatic force will be generated. When excited by the driving electrostaticthe horizontal force, direction. bending However, deformation because occurs the in azimuth the vibration angle beam, of the so vibration the vibration beam ismass less block than electrostatic force, bending deformation occurs in the vibration beam, so the vibration mass block oscillates90 degrees, in thethe verticalhorizontal driving direction. motion However, component because is also the generated. azimuth Therefore,angle of the in vibration the driving beam mode is oscillates in the horizontal direction. However, because the azimuth angle of the vibration beam is lessof the than gyroscope, 90 degrees, the vibrationthe vertical mass driving block hasmotion a three-dimensional component is also vibration generated. motion, Therefore, which consists in the less than 90 degrees, the vertical driving motion component is also generated. Therefore, in the drivingof the same mode reciprocating of the gyroscope, motion the frequency vibration in mass the horizontalblock has a direction three-dimensional and the driving vibration component motion, driving mode of the gyroscope, the vibration mass block has a three-dimensional vibration motion, whichmotion consists in the vertical of the direction, same reciprocating as shown in motion Figure9 a.frequency in the horizontal direction and the drivingwhich consistscomponent of themotion same in reciprocatingthe vertical direction, motion asfrequency shown in in Figure the horizontal9a. direction and the driving component motion in the vertical direction, as shown in Figure 9a. 2.4.2. Detection Mode 2.4.2. Detection Mode

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2.4.2.When Detection the gyroscope Mode is driven in driving mode and there is angular velocity input on the sensitive axis, a Coriolis force will be generated in the direction of detection, according to the When the gyroscope is driven in driving mode and there is angular velocity input on the sensitive principle of Coriolis force. This Coriolis force will cause torsional deformation of the vibration beam, axis, a Coriolis force will be generated in the direction of detection, according to the principle of Coriolis which will cause the vibration mass block to move up and down in the vertical direction, as shown force. This Coriolis force will cause torsional deformation of the vibration beam, which will cause the in Figure 9b. vibration mass block to move up and down in the vertical direction, as shown in Figure9b. 2.4.3. Working Condition 2.4.3. Working Condition The proposed tuning fork gyroscope uses the frequency mismatch model, and its working The proposed tuning fork gyroscope uses the frequency mismatch model, and its working frequency is the driving mode frequency. The amplitude–frequency response curves of the working frequency is the driving mode frequency. The amplitude–frequency response curves of the working modes of the gyroscope can be obtained by frequency response analysis (FRA). The theoretical modes of the gyroscope can be obtained by frequency response analysis (FRA). The theoretical amplitude–frequency response curves of the tuning fork gyroscope are shown in Figure 10. amplitude–frequency response curves of the tuning fork gyroscope are shown in Figure 10.

B Gain Peak of the Peak of the Vibration Amplitude Vibration Amplitude in Driving Mode in Detection Mode

Working Point of Gyroscope in Detection mode C

f Driving Resonace Detection Resonace Frequency Frequency FigureFigure 10. 10. TheThe theoretical theoretical amplitude–frequency amplitude–frequency response response curves of the tuning fork gyroscope.

As can bebe seenseen inin FigureFigure 10 10,, points points A A and and B areB are the the peaks peaks of theof the vibration vibration amplitude amplitude in driving in driving and anddetection detection curves, curves, respectively. respectively. The frequencies The frequencies of point of Apoint and pointA and B arepoint the B driving are the and driving detection and detectionresonance resonance frequencies frequencies of the gyroscope. of the gyroscope. The frequency The di frequencyfference between difference A and between B is defined A and as B the is definedfrequency as dithefference frequency of the difference tuning fork of gyroscope. the tuning Crossing fork gyroscope. point C insteadCrossing of detectionpoint C instead resonance of detectionfrequency resonance point B is frequency the working point point B is of the the workin gyroscopeg point in of detection the gyroscope mode. in This detection is why gyroscopesmode. This isoperating why gyroscopes in mismatched operating mode in mismatched have lower sensitivity mode have but lower higher sensitivity stability. but higher stability. Therefore, in the optimization design of the tuning fork gyroscope, it is necessary to select the operating frequency difference difference of the gyroscope reas reasonably.onably. On the premise of ensuring the stability of the working state of the gyroscope, it is is of great great significance significance to to reduce the frequency difference difference as much as possible in order to obtain the maximum sensitivity, so as to improve the performance of the gyroscope. 3. Fabrication Processing Technology 3. Fabrication Processing Technology The fabrication process consists of silicon structure processing, glass electrode substrate processing, The fabrication process consists of silicon structure processing, glass electrode substrate bonding processing, and packaging processing. processing, bonding processing, and packaging processing. 3.1. Fabrication Processing of Silicon Structure and Glass Electrode Substrate 3.1. Fabrication Processing of Silicon Structure and Glass Electrode Substrate The fabrication processing of the silicon structure, which combines wet and dry etching, can be seenThe infabrication Figure 11 processinga–f. The fabricationof the silicon processing structure, which of the combines glass electrode wet and substrate dry etching, can can be seenbe seen in inFigure Figure 11 11a–f.g–l. The fabrication processing of the glass electrode substrate can be seen in Figure 11g–l.

Micromachines 2019, 10, 813 9 of 17 Micromachines 2019, 10, x 9 of 17

FigureFigure 11.11. FabricationFabrication process process of theof siliconthe silicon structure structure and glass and electrode glass substrate:electrode (substrate:a) The processing (a) The of processingthe structure of startsthe structure with a double starts polishedwith a double silicon polished wafer. (b )silicon After high-temperaturewafer. (b) After high-temperature thermal oxidation, thermala layer ofoxidation, SiO2 is grown a layer on of the SiO silicon2 is grown wafer, andon the then silicon photolithography wafer, and then and developmentphotolithography processes and developmentare done on theprocesses back side are ofdone the siliconon the back wafer. side Part of ofthe the silicon photoresistant wafer. Part layer of the is photoresistant removed to prepare layer isfor removed the wet etchingto prepare in the for next the step.wet etching (c) After in removing the next partstep. of ( SiOc) After2, the removing remaining part SiO 2ofis SiO used2, asthe a

remainingnew mask, SiO and2 is then used the as wet a new etching mask, process and then is conducted the wet et onching the siliconprocess wafer. is conducted (d) Firstly, on thethe SiOsilicon2 on wafer.both sides (d) Firstly, is removed, the SiO and2 on a layerboth sides of aluminum is removed, is sputtered and a layer on theof aluminum back side ofis thesputtered silicon on wafer the asback the sidecut-o offf thelayer. silicon Then, wafer a layer as ofthe photoresistant cut-off layer. Then, layer isa usedlayer toof protectphotoresistant the aluminum layer is from used the to corrosionprotect the of aluminumthe developer. from At last,the thecorrosion second of photolithography the developer. and At development last, the second processes photolithography are done on the frontand developmentside of the silicon processes wafer. are Part done of photoresistanton the front side layer of the is removed silicon wafer. to prepare Part of for photoresistant the dry etching layer in the is removednext step. to (e )prepare After removing for the thedry photoresistant etching in the protective next step. layer (e) on After the back,removing dry etching the photoresistant is done on the protectivefront side layer continuously on the back, until dry the etching whole siliconis done wafer on the is front etched side to continuously the cut-off layer. until (f the) Removing whole silicon all of waferthe photoresistant is etched to the layer cut-off and thelayer. aluminum, (f) Removing the structure all of the processing photoresistant is completed. layer and (g) the The aluminum, processing theof thestructure electrode processing substrate is starts completed. with a ( glassg) The wafer, processing and alayer of the of electrod gold ise evaporated substrate starts on the with front a ofglass the wafer,glass wafer. and a (layerh) The of photolithographygold is evaporated and on developmentthe front of the processes glass wafer. are done (h) The on thephotolithography gold layer, and and part developmentof photoresistant processes layer isare removed. done on ( ithe) After gold removing layer, and part part of of the photoresistant Au, the remaining layer Auis removed. serves as the(i) Aftermask, removing and wet part etching of the is doneAu, the on remaining the glass waferAu serves to make as the the mask, gaps and and wet provide etching the is motion done on space the glassfor the wafer silicon to structuremake the (c).gaps (j ,kand) After provide removing the motion all of thespace photoresistant for the silicon layer structure and the (c). Au, (j a,k layer) After of removingaluminum all is of sputtered the photoresistant on the gap. layer Then, and the photolithographythe Au, a layer of andaluminum development is sputtered processes on the are donegap. Then,on the the aluminum photolithography layer. Part ofand photoresistant development layer processes is then are removed, done on and the the aluminum rest of the photoresistantlayer. Part of photoresistantlayer serves as layer the mask is then to prepareremoved, for and the the next rest step. of (thel) After photoresistant removing thelayer aluminum serves as without the mask mask to preparelayer protection, for the next the step. mask (l layer) After is removing removed andthe thealuminum electrode withou substratet mask is finished.layer protection, the mask 3.2. Bondinglayer is removed and Packaging and theProcess electrode substrate is finished.

3.2. BondingThe structure and Packaging and electrode Process substrate are bonded together with a narrow capacitive gap, which can increase the electromechanical coupling. After bonding, the gyroscopes are packaged in a ceramic The structure and electrode substrate are bonded together with a narrow capacitive gap, which chip carrier in a vacuum environment in order to minimize the Brownian noise ﬂoor to achieve better can increase the electromechanical coupling. After bonding, the gyroscopes are packaged in a performance. The entire device can be observed under an optical microscope, and some parts of the ceramic chip carrier in a vacuum environment in order to minimize the Brownian noise ﬂoor to structure can be observed by scanning electron microscope (SEM), as shown in Figure 12. achieve better performance. The entire device can be observed under an optical microscope, and some parts of the structure can be observed by scanning electron microscope (SEM), as shown in Figure 12.

Micromachines 2019, 10, 813 10 of 17 MicromachinesMicromachines 20192019,, 1010,, xx 1010 ofof 1717

Figure 12. Proposed gyroscopes were packaged in ceramic tubes. FigureFigure 12. 12. ProposedProposed gyroscopes gyroscopes were were packaged packaged in ceramic tubes.

4.4. PerformancePerformance TestingTesting TheThe performance performance testing testing of of gyroscopes gyroscopes in in ceramic ceramic tubes tubes mainly mainly includes includes modal modal testing testing and and zerozero biasbias testing. testing.

4.1. Circuit Signal Processing Technology 4.1.4.1. CircuitCircuit SignalSignal ProcessingProcessing TechnologyTechnology ThereThere is is a a detection detection electrode electrode andand aa pair pair ofof driving driving electrodeselectrodes belowbelow eacheach vibrationvibration mass.mass. mass. WhenWhen electrodeselectrodeselectrodes with withwith the the samethe samesame phase phasephase are connected areare connectedconnected together, thetogether,together, microelectromechanical thethe microelectromechanicalmicroelectromechanical gyroscope is gyroscopeequivalentgyroscope isis to equivalentequivalent a five-terminal toto aa five-terminalfive-terminal device [29]. devicedevice [29].[29]. AsAs can can be be seen seen in in Figure Figure 13,1313,, the device consists of of four capacitors andand one one common common terminal,terminal, which isis thethe siliconsilicon structurestructure ofof thethe gyroscope. gyroscope.C Cdtdt++ and CCdtdt- areare the the differential differential capacitances for the which is the silicon structure of the gyroscope. Cdt+ and Cdt-− are the differential capacitances for the driving axis, while Cst+st+ andand CCst-st areare the the differential differential capacitances capacitances for for the the sensing sensing axis. axis. Here, Here, Vd+V andd+ and Vd- driving axis, while Cst+ and Cst- are− the differential capacitances for the sensing axis. Here, Vd+ and Vd- Vared appliedare applied to the to driving the driving electrodes, electrodes, while while Vs+ andV sV+ s-and are Vapplieds are appliedto the sensing to the electrodes. sensing electrodes. (Where, are− applied to the driving electrodes, while Vs+ and Vs- are applied− to the sensing electrodes. (Where, CTV(Where,CTV standsstands CTV forfor stands capacitance/voltagecapacitance/voltage for capacitance/voltage converting,converting, converting, HPFHPF standsstands HPF stands forfor highhigh for pass highpass fi passfilterlter filter andand LPF andLPF LPFstandsstands stands forfor lowforlow low passpass pass filter.)filter.) filter.)

Figure 13. The equivalent model of the gyro circuit. FigureFigure 13.13. TheThe equivalentequivalent modelmodel ofof thethe gyrogyro circuit.circuit. The voltages applied to the diﬀerential capacitance are shown in the following equation: TheThe voltagesvoltages appliedapplied toto thethe differentialdifferential capacitancecapacitance areare shownshown inin thethe followingfollowing equation:equation:  =+ωω +  Vd+VVVd=+ =+Vdc dc+ V acacsinsinωωω dd tEt ++ E fdf dsinsin ω fd tf dt  VVVd+ dc acsin d tE fd sin fd t    VdVVV=− =−Vdc Vac sin ωωωd tEt −E f d sinsin ω f dtt  VVVddcacd− =−sinωω tE − fdfd sin t  −ddcacd− − fdfd (5)(5)  Vs+ ==E sin ωω t (5)  VEVEsfsfs+ = f s sinsinωf s t t   sfsfs+  V = E sin ω t sVE− =−f s sinωf s t VE− sfsfs− =−− sinω t  sfsfs ω where Vdc is the DC bias, Vacacsinωdt is the AC drive voltage, Efdfdsinωfdfdt and Efsfssin fsfst are the high wherewhere VVdc isis thethe DCDC bias,bias, VVacsinsinωωdtdt isis thethe ACAC drivedrive voltage,voltage, EEfdsinsinωωfdtt andand EEfssinsinωωfstt areare thethe highhigh frequency carriers in the driving and sensing axes. All the high frequency carriers come from the frequencyfrequency carrierscarriers inin thethe drivingdriving andand sensingsensing axesaxes.. AllAll thethe highhigh frequencyfrequency carrierscarriers comecome fromfrom thethe c pre-setpre-set outputoutput ofof thethe MicrocontrollerMicrocontroller UnitUnit (MCU).(MCU). So,So, thethe outputoutput voltagevoltage ofof thethe chargecharge amplifieramplifier ((VVc)) cancan bebe describeddescribed as:as:

Micromachines 2019, 10, 813 11 of 17

Micromachines 2019, 10, x 11 of 17 pre-set output of the Microcontroller Unit (MCU). So, the output voltage of the charge amplifier (Vc) can be described as: VVCVCVCVCC=−()/ + + + cddtddtsstsstf++ −− ++ −− (6) Vc = (Vd+Cdt+ + Vd Cdt + Vs+Cst+ + Vs Cst )/C f (6) After passing through the− high pass filter− (HPF− ) and amplification− − (Kh), the output voltage Vch can be described as: After passing through the high pass filter (HPF) and amplification (Kh), the output voltage Vch can be described as: VKEtCCKEtCC=−( sinωω Δ ) / − ( sin Δ ) / ch h fd fd d f h fs fs s f (7) V = (K E sin ω t∆C )/C (K E sin ω t∆Cs)/C (7) ch − h f d f d d f − h f s f s f After passing through the multiplier, the signal Vch is demodulated by the high-frequency After passing through the multiplier, the signal Vch is demodulated by the high-frequency driving driving and sensing carriers, respectively. So, the end output voltages Vdeo and Vseo can be described V V andas: sensing carriers, respectively. So, the end output voltages deo and seo can be described as:  2  VVKKECCdeo ==−()/2(KhKdeE Δ∆Cd)/2C f   deo− h de fdf d d f   (8)(8)  V =−= (K K E2 ΔC ) C  VKKECCseoseo()/2 hh dede fs∆ ss /2 ff  − f s

From EquationEquation (8),(8), wewe cancan seesee thatthat thethe outputoutput voltagesvoltagesV Vdeodeo andand VVseoseo are proportional to the variation of the driving and sensing capacitance, respectively. Thus, the variation of the driving and sensing capacitance can bebe eeffectivelyﬀectively extractedextracted andand separated.separated. In thethe closedclosed driving driving loop, loop, automatic automatic gain gain control control (AGC) (AGC) technology technology is used is to used ensure to theensure stability the ofstability the driving of the voltage. driving Thevoltage. high The frequency high frequency carrier signal carrier of thesignal driving of the voltage driving is voltage applied is to applied modulate to themodulate signal the of thesignal high of frequency the high frequency carrier signal. carrie Then,r signal. the Then, output the signal output on signal the common on the common terminal isterminal demodulated is demodulated with this with carrier this signal, carrier and signal the, information and the information for the driving for the loop driving can beloop obtained. can be Theobtained. schematic The schematic diagram of diagram the closed of drivingthe closed loop driving control loop is shown control in is Figure shown 14 in. (Where,Figure 14. C/V (Where, stands forC/V capacitance stands for /capacitance/voltagevoltage converting, converting, PID stands forPID Proportion stands for IntegralProportion Diﬀ Integralerential Differential and REF stands and forREF reference.) stands for reference.)

Common Terinal C/V HPF Detection Electrodes Carrier Drive Electrodes  LPF

 Inverting

Inverting Shifting Comparator

PID  Filter Comparator

REF

Figure 14. The schematic diagram of the closed driving loop control.

In order toto separateseparate thethe detectiondetection looploop informationinformation from thethe commoncommon terminalterminal and reduce thethe influenceinfluence of low-frequencylow-frequency noise, the high-frequency detection carrier is applied to thethe detectiondetection electrodes. TheThe detectiondetection capacitance capacitance variation variation signal sign isal modulated is modulated to the to high the frequencyhigh frequency of the carrierof the signal,carrier andsignal, the and useful the signaluseful and signal the and low-frequency the low-frequency noise are noise successfully are successfully separated. separated. The firstfirst demodulation with the high-frequency carrier separates the useful signal from other signals atat thethe common common terminal. terminal. The The frequency frequency of theof obtainedthe obtained signal signal is the frequencyis the frequency of the applied of the ACapplied driving AC voltage.driving voltage. The output The signaloutput after signal first af demodulationter first demodulation is demodulated is demodulated by the AC by drivingthe AC voltagedriving forvoltage the second for the time, second and time, the DC and voltage the DC signal voltage corresponding signal corresponding to the input to angularthe input velocity angular is obtained,velocity is as obtained, shown in as Figure shown 15 in. Figure 15.

Micromachines 2019, 10, x 12 of 17

First Time Second Time Common Demodulation Demodulation Terinal Carrier Vacsin(ωdt) C/V Vout Micromachines 2019, 10, 813 HPF LPF LPF 12 of 17 Micromachines 2019, 10, x 12 of 17

Figure 15. Schematic diagram of weak capacitance detection.

4.2. Modal Testing Frequency response analysis (FRA) is used to perform modal testing of the proposed First Time Second Time gyroscope, and the results are shown in Figure 16. The modal testing is an important part of the Demodulation Demodulation performance testing.Common On the one hand, the natural vibration frequencies of driving and detection Terinal Carrier V sin(ω t) modes can be obtained, and the working state of the gyroscope can acbe accuratelyd detected. On the other hand, the quality C/Vfactor (Q) of the driving and detection modes can be calculated according to Vout the modal test curves, and the vacuumHPF situation of LPFthe gyroscope canLPF be obtained, which provides an important reference for subsequent performance testing.

According to the characteristics of the micro-gyroscope proposed in this paper, a method combing electrostatic FigureFigureforce 15.excitation15. SchematicSchematic and diagramdiagram capaci ofoftance weakweak capacitancecapacitancedetection detection.isdetection. used for modal testing. A frequency response analyzer is used to apply sweep excitation on driving and detection electrodes, 4.2.4.2. Modal Testing and the response of the gyro to the signal is observed. The modal frequencies and Q values are obtainedFrequencyFrequency from responsetheresponse frequency analysis analysis response (FRA) (FRA) is analysis used is used to performcurves. to perform modalThe frequency testingmodal oftesting theresponse proposed of analyzerthe gyroscope,proposed is a FRA5087andgyroscope, the results from and Negative are the shown results Feedback in are Figure shown (NF) 16 . incompany. The Figure modal 16. Its testing Thefrequency modal is an resolution importanttesting is isan part 0.1 important ofMHz, the performancewhich part meetsof the thetesting.performance test requirements On the testing. one hand, forOn the the the gyroscope one natural hand, vibration [30]. the natural frequencies vibration of frequencies driving and of detection driving modesand detection can be obtained,modesThe can quality and be theobtained, factor working andof the state the gyroscope working of the gyroscope state is calcul of th caneated gyroscope be in accurately the can–3dB be detected. bandwidth.accurately On detected. theThe other frequency On hand, the responsetheother quality hand, in factor thethe driving quality (Q) of directionfactor the driving (Q) is of shown andthe driving detection in Figure and modes 16a, detection the can resonance bemodes calculated can frequency be accordingcalculated is 2912.33 to according the Hz, modal and to thetestthe quality curves,modal test andfactor curves, the is vacuum 12,414. and the situationThe vacuum frequency of thesituation gyroscoperesponse of the in can gyroscopethe be detection obtained, can direction whichbe obtained, provides is shown which an importantin provides Figure 16b,referencean important the resonance for subsequent reference frequency for performance subsequent is 3005.97 testing. performanceHz, and the quality testing. factor is 461.78. According to the characteristics of the micro-gyroscope proposed in this paper, a method combing electrostaticGain(mV) force excitationPhase(deg) and capacitanceGain(mV) detection is usedPhase(deg) for modal testing. A Gain 160 1.6 Gain frequency response0.4 analyzer is used to applyPhase -40 sweep excitation on driving and detection electrodes, and the response of the gyro to the signal is observed. The modal frequencies Phase 120 and Q values are -80 obtained from the frequency response analysis curves.1.2 The frequency response analyzer is a 0.3 80 FRA5087 from Negative Feedback (NF) company.-120 Its frequency resolution is 0.1 MHz, which meets the test requirements0.2 for the gyroscope [30]. 0.8 40 The quality factor of the gyroscope is-160 calculated in the –3dB bandwidth. The frequency (fd=2912.33Hz, Qd=12414) (fs=3005.97Hz, Qs=461.78) 0 response in the 2912.0driving direction 2912.2 2912.4is shown 2912.6 in Figure 16a,3000 the resonance 3005 3010frequency 3015 is 2912.33 Hz, and the quality factor is 12,414. The frequency response in the detection direction is shown in Figure 16b, the resonance frequency(a) Driving is 3005.97 mode Hz, and the quality (factorb) Detection is 461.78. mode

Gain(mV)Figure 16. ModalModalPhase(deg) testing of the Gain(mV) proposed gyroscope. Phase(deg) Gain 160 -40 1.6 Gain According to0.4 the characteristics of the Phase micro-gyroscope proposed in this paper, a method combing 4.3. Zero Bias Testing Phase 120 electrostatic force excitation and capacitance detection-80 is used for modal testing. A frequency response 1.2 analyzerThe iszero used bias0.3 to testing apply sweep is measured excitation at room on driving temperature, and detection and the electrodes, bias stability and the80of sample response reaches of the aboutgyro to 1.3°/h, the signal as shown is observed. in Figure The 17. modal frequencies-120 and Q values are obtained from the frequency 40 response analysis0.2 curves. The frequency response analyzer0.8 is a FRA5087 from Negative Feedback (NF) -160 company. Its frequency(fd=2912.33Hz, resolution isQd 0.1=12414) MHz, which meets( thefs=3005.97Hz, test requirements Qs=461.78) for0 the gyroscope [30]. The quality2912.0 factor of 2912.2 the gyroscope 2912.4 is calculated 2912.6 in the3000 –3dB 3005 bandwidth. 3010 The 3015 frequency response in the driving direction is shown in Figure 16a, the resonance frequency is 2912.33 Hz, and the quality factor is 12,414. The frequency(a) Driving response mode in the detection direction(b) Detection is shown mode in Figure 16b, the resonance frequency is 3005.97 Hz, and the quality factor is 461.78. Figure 16. Modal testing of the proposed gyroscope. 4.3. Zero Bias Testing 4.3. Zero Bias Testing The zero bias testing is measured at room temperature, and the bias stability of sample reaches The zero bias testing is measured at room temperature, and the bias stability of sample reaches about 1.3◦/h, as shown in Figure 17. about 1.3°/h, as shown in Figure 17.

Micromachines 2019, 10, 813 13 of 17 Micromachines 2019, 10, x 13 of 17

-0.5520

-0.5521

-0.5522

-0.5523

-0.5524 Voutput (V) Voutput (V) -0.5525

-0.5526

-0.5527 0 600 1200 1800 2400 3000 3600 Time (s) Figure 17. Zero bias output of the sample.

Allan variance is used to analyze the bias stability.stability. The standard definition deﬁnition of bias instability used byby inertialinertial sensor sensor manufacturers manufacturers is theis the minimum minimum point point on the on Allan the Allan variance variance curve. Thecurve. system The systemdemonstrates demonstrates a bias instability a bias instability of 0.589◦ /ofh and0.589°/h an angular and an random angular walk random (ARW) walk of (ARW) 0.038◦/√ ofh, 0.038°/ as shown√h, asin Figureshown 18in. Figure 18.

Angle Random Walk= 0 0.038 deg/√h 10 0.038 deg/√h Allan deviation (deg/h) Allan deviation (deg/h) Bias Instability= 0.589 deg/h

0 1 2 3 100 101 102 103 Integration interval (s) Figure 18. Allan deviation of the sample.

As cancan bebe seen seen from from the the performance performance results, results, compared compared to other to other reported reported high-performance high-performance MEMS MEMSgyroscope, gyroscope, the performance the performance of the proposedof the proposed tuning tuning fork gyroscope fork gyroscope is not goodis notenough. good enough. The noise The noiselevel oflevel the of gyroscope the gyroscope is critical is critical to the performance,to the performance, and the and low the noise low level noise of thelevel gyroscope of the gyroscope is one of isthe one reasons of the for reasons its poor for performance. its poor performance. So, the analysis So, ofthe gyroscope analysis noiseof gyroscope is carried noise on, which is carried is helpful on, whichfor performance is helpful for improvement. performance improvement.

5. Noise Analysis The resolution and minimum bias stability of th thee MEMS gyroscope are determined by the noise level ofof the the angular angular velocity velocity output output signal. signal. The noiseThe ofnoise the gyroscopeof the gyroscope system consists system of consists the mechanical of the mechanicalthermal noise thermal from thenoise silicon from structure the silicon and structure the circuit and noise the circuit from the noise detection from the circuit. detection circuit. 5.1. Mechanical Thermal Noise 5.1. Mechanical Thermal Noise Mechanical thermal noise is the main noise resource of the MEMS gyroscope. It is caused by Mechanical thermal noise is the main noise resource of the MEMS gyroscope. It is caused by irregular thermal motions of gas molecules around inertial mass and molecules inside the structure, irregular thermal motions of gas molecules around inertial mass and molecules inside the structure, and is directly related to the damping of the system. The greater the damping of system, the greater and is directly related to the damping of the system. The greater the damping of system, the greater the mechanical thermal noise. The equivalent force of the mechanical thermal noise in the MEMS the mechanical thermal noise. The equivalent force of the mechanical thermal noise in the MEMS gyroscope can be described as [31]: gyroscope can be described as [31]: p Fmtn = 4kBTcB (9) F = 4kTcB (9) mtn B

Micromachines 2019, 10, x 14 of 17

Micromachines 2019, 10, 813 14 of 17 where kB is the Boltzmann constant, T is the absolute temperature in degrees Kelvin, c is the damping coefficient of the system, and B is the bandwidth of the gyroscope. whereTheMicromachineskB equivalentis the Boltzmann2019, 10 angular, x constant, velocityT ofis the the mechanical absolute temperature thermal noise in degrees in the Kelvin,gyroscopec is in the 14this dampingof 17 paper cancoe ﬃbecient described of the as: system, and B is the bandwidth of the gyroscope. where kB is the Boltzmann constant, T is the absolute temperature in degrees Kelvin, c is the damping The equivalent angular velocity of the mechanical thermal noise in the gyroscope in this paper coefficient of the system, and B is the bandwidth1 of thekT gyroscope.ω B can be described as: Ω= bs (10) The equivalent angular velocity of theTMN mechanicalx smQω thermal2 noise in the gyroscope in this paper 10 k TdsωsB can be described as: Ω = b (10) TMN 2 x0 mω Qs where x0 is the dynamic displacement along the drivingω d direction, ɷd and ɷs are the resonant Ω=1 kTbs B TMN 2 (10) frequencieswhere x is the of dynamicdriving and displacement detection modes, along the m drivingis xthe mQequivalent direction,ω ωvibrationand ωs aremass, the and resonant Qs is frequenciesthe quality 0 0 ds d factorof driving of the and detection detection mode. modes, Accordingm is the equivalentto Equation vibration (10), reducing mass, andthe mechanicalQs is the quality thermal factor noise of the of where x0 is the dynamic displacement along the driving direction, ɷd and ɷs are the resonant thedetection gyroscope mode. so According as to improve to Equation the (10),performanc reducinge thecan mechanical be achieved thermal by noiseimproving of the gyroscopethe driving so frequencies of driving and detection modes, m is the equivalent vibration mass, and Qs is the quality displacementas to improve and the performanceequivalent vibr canation be achieved mass and by increasing improving the the Q drivings. displacement and equivalent factor of the detection mode. According to Equation (10), reducing the mechanical thermal noise of vibrationthe gyroscope mass and so increasing as to improve the Qs .the performance can be achieved by improving the driving 5.2. Noise in the Detection Circuit displacement and equivalent vibration mass and increasing the Qs. 5.2. Noise in the Detection Circuit The minimum signal level that a circuit can handle correctly is determined by the noise of the detectionThe5.2. Noise minimumcircuit. in the The Detection signal greater levelCircuit the thatnois e a of circuit the circuit, can handle the poorer correctly the abil is determinedity of the circuit by the is noiseto detect ofthe or processdetection smallThe circuit. minimum signals, The greaterand signal the level the poorer noisethat thea ofcircuit theperforma circuit, can handlence the of poorercorrectly the gyroscope the is abilitydetermined system. of the by circuit Inthe order noise is to toof detectanalyzethe or theprocess circuitdetection small noise circuit. signals, of the The andgyroscope, greater the poorerthe thenois thenoisee of performancethe model circuit, of the the poorer of gyroscope the gyroscopethe abil systemity of system. the needs circuit In to is order tobe detect established. toanalyze or Thethe circuitcircuitprocess noisenoise small of ofsignals, thethe gyroscope,gyroscope and the poorer theis mainly noisethe performa modelrelatednce of to the ofthe the gyroscope detection gyroscope systemcircuit, system. so needs In the order tonoise beto analyze established.analysis in theThe detection circuitthe circuit noise circuit noise of theof is the gyroscopefocused gyroscope, on is this. mainlythe noise The related modelmain toofnoise the gyroscope detectionsources of circuit,system the gyroscope needs so the to noise be in established. analysisthe detection in the The circuit noise of the gyroscope is mainly related to the detection circuit, so the noise analysis in circuitdetection can circuit be seen is focusedin Figure on 19. this. The main noise sources of the gyroscope in the detection circuit can the detection circuit is focused on this. The main noise sources of the gyroscope in the detection be seen in Figure 19. circuit can be seen in Figure 19. Noise in C/V Noise in HPF Noise in Switch Noise in LPF

C/V Noise in C/V Noise in HPF Noise in Switch Noise in LPF Carrier Switch C/V HPF Demodulation LPF Carrier Switch HPF Demodulation LPF Common Terinal Common Carrier Terinal Carrier Noise in Switch Noise in LPF Noise in Switch Noise in LPF

Second Switch Vout Vacsin(ωdt) DemodulationSecond Switch LPF Vout Vacsin(ωdt) Demodulation LPF

FigureFigureFigure 19. 19. 19.TheThe The main main main noise noise noise sources sourcessources of of the the gyroscopegyroscope gyroscope in in indetection detection detection circuit. circuit. circuit.

AsAs can As bebecan seenseen be seen inin Figure Figurein Figure 19 19,, the19, the the switch switch switch demodulation demodulation demodulation is is conductedis conducted conducted at at a ata high high a high frequency, frequency, frequency, soso thethe so noise the noisegeneratednoise generated generated by the by switch theby the switch is restrainedswitch is isrestrained restrained after passing afterafter throughpassing through thethrough low the pass the low filter.low pass pass The filter. chargefilter. The The amplifiercharge charge is amplifierlocatedamplifier at is the located is front located endat theat of the thefront front detection end end of of the circuit, the detectdetect soion the circuit,circuit, noise generatedso so the the noise noise by generated the generated charge by amplifiertheby chargethe charge is the amplifier is the main circuit noise. amplifiermain circuit is the noise. main circuit noise. The noise model of the front-end charge amplifier is established in Figure 20. TheThe noise noise model model of of the front-end charge amplifier amplifier is established in Figure 2020..

Cf Cf iRf iRf Gyroscope Rf Gyroscope Rf

eo Cgro Amplifier Vi inn eo Cgro Amplifier V inn i en inp en inp Figure 20. The noise model of the front-end charge amplifier in the detection circuit.

FigureFigure 20. 20. TheThe noise noise model model of of the the front-end front-end charge charge amplifier ampliﬁer in in the the detection detection circuit. circuit.

Micromachines 2019, 10, 813 15 of 17

The noise of the front-end charge amplifier mainly includes three parts: equivalent input voltage, circuit noise, and resistance thermal noise. Capacitors do not produce noise, but instead limit the frequency bandwidth of the output voltage. Therefore, the total output noise of the charge amplifier is contributed by the operational amplifier and resistor. Because of the irrelevance of the noise, the total power density of the output noise can be calculated as: 2 !2 ! Cgro 4kT 1 e2 = e2 1 + + i 2 + (11) oc n nn 2 C f R f jωC f where Cgro is the sum of the driving voltage and detection capacitance of the gyroscope, Cf is the feedback capacitance of the charge amplifier, and Rf is the feedback resistor of the charge amplifier. If eoc is equivalent to capacitive noise density cnc, then eoc can be described as:

2 ! C f + Cgro 4kT 1 c2 = e2 + i2 + (12) nc n 2 nn 2 R 2 E f s f jω f s E f s

According to Equation (12), the main measures to reduce circuit noise are as follows:

(a) Select a better operational ampliﬁer with lower noise en. (b) Increase the frequency of carrier ωf2. (c) Decrease the feedback capacitor of the charge ampliﬁer Cf. (d) Improve the amplitude of carrier Ef2.

6. Conclusions The design, simulation, fabrication, and experimentation of a novel split-mode, micromachined tuning fork gyroscope has been presented in this paper. Increasing the spindle azimuth of the vibration beam of the gyroscope can not only improve the driving displacement, but can also reduce the vibration gap and enhance the SNR of the sensor. The impact factors of the spindle azimuth of the vibration beam were designed and analyzed. The fabrication processes were demonstrated, including the manufacture of the vibration structure, glass substrate, anodic bonding, and vacuum packaging process. Finally, performance testing of the gyroscope in a ceramic tube was conducted. The zero-rate bias instability and ARW were obtained as 0.589◦/h and 0.038◦/√h from measurements at room temperature, respectively. After analyzing the noise of the tuning fork gyroscope, there is still a lot of work to do. On the one hand, it is necessary to improve the processing quality to reduce the mode coupling and zero bias. On the other hand, a better operational ampliﬁer with lower noise should be applied to improve the overall signal-to-noise ratio of the gyroscope and further improve the performance of the gyroscope.

Author Contributions: Conceptualization, Z.H. and D.X.; methodology, F.O. and M.Z.; software, Y.K. and T.M.; validation, Q.X. and F.O.; formal analysis, Z.H., D.X., and X.W.; investigation, Q.X. and Z.H.; resources, Z.H., M.Z., and X.W.; data curation, Q.X. and Y.K.; writing—original draft preparation, Q.X.; writing—review and editing, Q.X.; visualization, Z.H. and T.M.; supervision, D.X. and X.W.; project administration, D.X. and X.W.; funding acquisition, D.X. and X.W. Funding: This research received no external funding. Acknowledgments: The authors would like to thank the editors and the reviewers for their help. Conﬂicts of Interest: The authors declare no conﬂict of interest. Micromachines 2019, 10, 813 16 of 17

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