PracticalMEMS Chap3 Accelerometers - Kaajakari
Transcript of PracticalMEMS Chap3 Accelerometers - Kaajakari
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Practical MEMS
Chapter 3: Accelerometers
http://www.kaajakari.net/PracticalMEMS
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Micromachined accelerometers
• The “second” MEMS product (first was pressure sensors).• Applications:
– Crash detectors for air bag deployment. Over 6,000 lives saved in US.– Low-G sensors are used for active suspensions and vehicle stabilization
controls. – Motion based user interfaces (e.g. game consoles, cell phones)– Step counters, running speed and distance.– Digital cameras to determine the picture orientation.– Free fall detection to protect laptop hard drives
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Principle of operation
• A proof mass is attached to frame with a spring.
• When the frame is accelerated, the proof mass follows the frame motion with a lag.
mk
γ
mx
fx
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Frequency response
mk
γ
mx
fxmf xxx −=
fxmkxtx
txm &&=+
∂∂
+∂∂ γ2
2
ksmsxm
x f
++=
γ2
&&
Equation of motion:
The proof mass displacement relative to the frame is proportional to the acceleration!
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Amplitude of the response
20ωff x
kxm
x&&&&
=≈ ff xx
x =≈ 2ω&&
2
0
2
2
2
0
1
/
+
−
=
ωω
ωω
Q
kxmx f&&
wheremk
=0ω andγ
ω mQ 0=
|x|
Excitation frequency
low frequency response
high frequency response
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Changing the resonant frequency
•Lowering ω0 improves low frequency response but does not affect high frequency response.
•Overall, lowering ω0 helps.•Taken to extreme ω0 = 1-2 Hz! (Macroscopic seismometers).
•For MEMS typically ω0 > 50 HZ.
100 101 102 103 10410-9
10-8
10-7
10-6
10-5
10-4
Frequency[Hz]
|X|
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Scaling laws for accelerometers
What happens when all dimensions are reduced 10x?
mk
γ
mx
fx
fmf xkmxx &&=−
100
10
000,1
mfmf
xxxx
kk
mm
−→−
→
→
(Analog devices accelerometers measure 0.1 Å displacements!)
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0 2 4 60
0.5
1
1.5
t⋅f0
x[F/
k]
Q = 0.5
Q = 0.2
Q = 2
Time domain response
Critical damping or over damping preferred for clean response
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Sensing principles
• Piezoresistive– Stress sensitive resistors integrated in the springs– Robust– Noisy, high power, and large temperature dependency
• Capacitive– Direct measurement of displacement– Low power, low noise– Small capacitance measurement is difficult
• Piezoelectric– Self generating– Signal proportional to change in stress – no dc signal!
• Magnetic• Optical
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mk
γ
mx
fx [ ]Hz/m/s4
:onaccelerati equivalent Noise
20
mQTkx B
nω
=&&
Noise equivalent acceleration(spectral density)
xmFTkF
x
Bn
&&&& =
= γ4
:forceon acceleratiapparent andgenerator force noise Equate
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mk
γ
mx
fx
Noise equivalent acceleration(rms acceleration)
kTkx
Tkkx
B
B
=⇔
=
2rms
2rms 2
121
fmf xkmxxx &&=−=
mTk
mTkkx BB
20
2rms
ω==&&
Total rms noise depends only on mass and resonant frequency!
(1)
(2)
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A2 =1k
A1 = m
F n =√4kBTγ
x xF
System level noise model
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C1C2
anchorfolded spring
proof mass
Quality factor
Electrode capacitance
Spring constant
Mass
Resonant frequency
Parameter
3-4Q
pF0.1C0
N/m2k
nkg0.1m
kHz22f0
UnitsValueSymbol
APPLIED ACCELERATION
TOP VIEWTOP VIEW
MASS
SPRING
DENOTES ANCHOR
FIXED SENSING FINGERS
C1C2
C1C2
MASS
Surface micromachined accelerometer
HzmG/2.0=nx&&
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ADXL50 Accelerometer• +/-50G• Polysilicon MEMS &
BiCMOS• 3x3mm die
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1000 µm
Quality factor
Electrode capacitance
Spring constant
Mass
Resonant frequency
Parameter
0.1Q
pF5C0
N/m50k
µkg1m
kHz1f0
UnitsValueSymbol
380 µm
proof masselectrode
electrode
Bulk micromachined accelerometer
HzG/3
:onacceleratiequivalentNoise
µ=nx&&