Sponsored by the IEEE Sensors Council, www.ieee-sensors.org

SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013

SENSORS 2013

 

SENSORS 2013

SENSORS 2013

 

 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.

SENSORS 2013

  

SENSORS 2013

 

acor = −2Ω× vdrv

   acor

SENSORS 2013

 

 

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 =

SENSORS 2013

  

  

  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)

=Qdrvmω0drv

2 ∠X( jω)Felecx ( jω)

= −90º

X( jω)Felec ( jω)

=1

m

1

−ω 2 +ω0drvQdrv

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

SENSORS 2013

  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 +

ω0snsQsns

jω0drv +ω0sns2

 

SENSORS 2013

  

If ω0drv

SENSORS 2013

   

Robert Bosch GmbH, single-axis gyroscope U. Michigan, Ring gyroscope

   

  

   

 

J. Marek, IEEE, ISSCC 2010

SENSORS 2013

 

  

    

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

SENSORS 2013

• 

-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

SENSORS 2013

• 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

Finy

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)+ω02Q2

q2 I (t)+b21mq1(t)+ω02

2 q2 I (t) = 0+b21mq1(t)

•  q2 I (ω)q1(ω) ω=ω01=ω02

= −b21Q2mω01

∠00

• 

q2c (ω)q1(ω) ω=ω01=ω02

=2λQ2ω01

Ω( ′ω )∠00

q2c (t)+ω02Q2

q2c (t)+ω022 q2c (t) = 2λΩ(t)q1(t)= 2λΩ(t)q1(t)

• 

SENSORS 2013

• 1

Q=

1

QSFD+

1

QTED+

1

Qanchor+

1

Qsurface+

1

Qintrinsic

1

QSFD∝μeffg03

1

1+jωωc

1

QTED=

Eα 2 T0Cυ

⎛

⎝⎜

⎞

⎠⎟

ωmech τ n1+ ωmech τ n( )

2 fnn

∑ 1Qanchor

=1

2πWresonatorΔWanchor

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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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SENSORS 2013

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Sponsored by the IEEE Sensors Council, www.ieee-sensors.org

SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013