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Sponsored by the IEEE Sensors Council, www.ieee-sensors.org
SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013
SENSORS 2013
SENSORS 2013
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Source: Yole Développement, “STMicro L3G3250A Reverse costing”, 2012
Source: Seeger, et. al. "Development of High-Performance, High-Volume Consumer MEMS Gyroscopes.” Solid-State Sensor, Actuator and Microsystems Workshop, Hilton Head Island. 2010.
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acor = −2Ω× vdrv
acor
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m∂2y∂t2
+ by∂y∂t+ ky y = Felecy − 2mλΩZ
∂x∂t
∂y∂t+m
∂2y∂t2 y y = Z
∂x∂t
m∂2x∂t2
+ bx∂x∂t+ kx x = Felecx + 2mλΩZ
∂y∂tZ
∂y∂t
∂x∂t+m
∂2x∂t2 x x =
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Ω θ
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Ω
MODE 1 MODE 2
m∂2x∂t2
+ bx∂x∂t+ kx x = Felecx m
∂2y∂t2
+ by∂y∂t+ ky y = −2mλΩZ
∂x∂t
Ω
Fcor = −2mλ Ω×∂x∂t
SENSORS 2013
Amp TransducerTransducer
xFelecx
ΩzDrive System
Fcor y∂/∂t
vx
Sense System
Amp TransducerTransducer
Felecx
Drive SystemDrive System
m∂2x∂t2
+ bx∂x∂t+ kx x = Felecx
ω ω0drvX( jω)Felecx ( jω)
=Qdrv
mω0drv2 ∠
X( jω)Felecx ( jω)
= −90º
X( jω)Felec ( jω)
=1
m
1
−ω 2 +ω0drv
Qdrv
jω +ω0drv2
Qdrv =kx m
bxω0drv =
kxm
SENSORS 2013
Micralyne DRIE etched comb-drive structures
dC
dx=ε ⋅2n ⋅ tg0
Device Overview DDDeevviiiccceee OOOOvvvveeerrrrvvvvvvvviiiieeewwwww Electrode
Resonating Proof-Mass
40-60µm
Capacitive Gap
GATech/Qualtré’s HARPSS parallel-plate gaps
dC
dx=
ε ⋅w ⋅ t
g0 − x( )2≈ε ⋅w ⋅ tg02
Micralyne DRIE etched comb drive structures
Motor
Stator
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vdrv Ω
Amp TransducerTransducer
xFelecx
ΩzDrive System
Fcor y∂/∂t
vx
Sense System
ΩzΩΩ
FFcor yyvxx
S S tSense System
m∂2y∂t2
+ by∂y∂t+ ky y = Fcor Fcor = 2mλΩZ
∂x∂t
ω0sns ω0drv
Y ( jω)X( jω) ω=ω0 drv
= 2λΩjω0drv
−ω0drv2 +
ω0sns
Qsns
jω0drv +ω0sns2
SENSORS 2013
If ω0drv << ω0sns:
y
x split
≈ 2λΩZ
ω0drv
ω0sns2
If ω0drv = ω0sns:
y
x matched
= 2λΩZ
Q
ω0
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Robert Bosch GmbH, single-axis gyroscope U. Michigan, Ring gyroscope
J. Marek, IEEE, ISSCC 2010
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SF∝xdrvω0drv
ω0sns2 −ω0drv
2( )2+ω0sns2 ω0drv
2
Qsns
dC
dxVP
SensorDynamics, 3-axis gyroscope Source: http://www.i-micronews.com/news/Generation-MEMS-gyroscopes-inertial-combo-sensors-SensorDyn,6375.html
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Q = 77,000
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Rm =2π ⋅Meff ⋅ g0
4 ⋅ fresε0 ⋅Aelec ⋅VP( )2 ⋅Q
frff es⋅ g04 ⋅
⋅Q
Mefe fff [Ω]
SF =2π ⋅λ ⋅ε0 ⋅Aelec ⋅VP ⋅Q
180 ⋅α ⋅ g0
⋅Q⋅ g0
[A/(º/s)]
MNEΩ =180 ⋅απ ⋅λ ⋅ g0
kB ⋅Tπ ⋅Meff ⋅ fres ⋅Q⋅Q⋅ frff es⋅ g0 Mefe fff
[(º/s)√Hz]
BW =fres2Q
frff es2Q
[Hz]
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• •
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•
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X-Axis Axl. Response
Y-Axis Axl. Response
Z-Axis Axl. Response X-Axis Gyro Response X Axis Gyro Response
Q ≈ 28,000
Y-Axis Gyro Response
Q ≈ 28,000
Z-Axis Gyro Response
SSSSEEEENNNNSSSSOOOORRRRS
Q ≈ 118,000
Resonator
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m11 q1(t)+ d11 q1(t)+ k11 q1(t) = −2λm22 q2 (t)Ω(t)
m22 q2 (t)+ d22 q2 (t)+ k22 q2 (t) = 2λm11 q1(t)Ω(t)
ω01=
k11m11
=ω02 =k22m22
Δω0 = 0
k22 ≠ k11
m22 ≠m11
ω01≠ω02
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
Mag
ntid
ue [d
B]
Frequency [Hz]
Mode 1
Mode 2
Δω0 ≠ 0
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•
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
Mag
ntid
ue [d
B]
Frequency [Hz]
Mode 1
Mode 2
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
Mag
ntid
ue [d
B]
Frequency [Hz]
Mode 1
Mode 2
k11elec =εAg03
VP −VT , j( )j=1
l
∑2
Spring softening
ω01=k11mech − k11elec
m11
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• Ωz
m
k1, b1
x
k1, b1
k2, b2
k2, b2
Fin
m
k1, b1 k1, b1
k2, b2
k2, b2
y
Fcoriolis
Fcor = 2mλΩZ
∂x∂t
•
m
xk12, b12
Fin
y
k12, b12k12, b12
k12, b12
Damping coupling Stiffness coupling
mq1(t)+ d11 q1(t)+ d12 q2 (t)+ k11 q1(t)+ k12 q2 (t) = −2λmq2 (t)Ω(t)
Coriolis coupling
mq2 (t)+ d22 q2 (t)+ d21 q1(t)+ k22 q2 (t)+ k21 q1(t) = 2λmq1(t)Ω(t)
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•
Felec
Drive Mode
q2QModeCoupling
k21
Sense Mode
q1 FQ
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
Mag
ntid
ue [d
B]
Frequency [Hz]
Mode 1
Mode 2
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
Mag
ntid
ue [d
B]
Frequency [Hz]
Mode 1
Mode 2
∠q2Qq1
≈ −90º
•
2000 2 37252500 72530002 2 00 2 3000 7252 500 72500 7253000 725352500 7253000 72535
•
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•
q2 I (t)+ω02
Q2
q2 I (t)+b21mq1(t)+ω02
2 q2 I (t) = 0+b21mq1(t)
• q2 I (ω)q1(ω) ω=ω01=ω02
= −b21Q2
mω01
∠00
•
q2c (ω)q1(ω) ω=ω01=ω02
=2λQ2
ω01
Ω( ′ω )∠00
q2c (t)+ω02
Q2
q2c (t)+ω02
2 q2c (t) = 2λΩ(t)q1(t)= 2λΩ(t)q1(t)
•
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• 1
Q=
1
QSFD
+1
QTED
+1
Qanchor
+1
Qsurface
+1
Qintrinsic
1
QSFD
∝μeff
g03
1
1+jωωc
1
QTED
=Eα 2 T0Cυ
⎛
⎝⎜
⎞
⎠⎟
ωmech τ n1+ ωmech τ n( )2
fnn
∑ 1
Qanchor
=1
2πWresonator
ΔWanchor
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•
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ax, ay, az vx, vy, vz dx, dy, dz Position
Orientation Ωx, Ωy, Ωz ϕx, ϕy, ϕz
• •
ϕx, ϕy, ϕz
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• •
λ2=27
90≈ 0.3
27º
90º
• •
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•
• • •
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•
q2q1= tan2θ
• • •
• •
•
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• •
Vib
ratio
n A
mpl
itude
Time [s]
Mode 1
Mode 2
• •
•
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•
•
•
• • •
•
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Sponsored by the IEEE Sensors Council, www.ieee-sensors.org
SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013