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TRANSCRIPT
Capacitive sensors and their readout electronics
Aarne Oja
VTT Information TechnologyMicrosensing
Contents
• What it’s all about: micromachined capacitive accelometer as an example• Motivation for capacitive MEMS sensors (goodies)• Capacitive readout schemes
• AC readout (displacement measurement)• Direct readout (velocity measurement)• Readout using a tuned circuit• Capacitive sensors based on loss factor measurement• Resonating capacitive sensors
• Basic sensor terminology• Brownian noise of capacitive sensors• Electrostatic actuation (the concept of transducer)
• CV curve of a capacitive transducer• Pull-in voltage
• Measurement techniques related to capacitive sensors• Bridge measurement• Nonlinearity of the capacitive sensor• Force feedback• Guarding against stray capacitances
Motivation for capacitive sensors
• Low power consumption• High resolution• Small temperature coefficient (e.g., in capacitive MEMS sensors)• Possibility for high-volume manufacturing (e.g., by using MEMS
technology)• Potential for low cost• Potential for monolithic integration with readout electronics• Possibility to reuse of IP blocks (i.e., designs) both in IC and MEMS parts• In capacitive MEMS sensors, the dynamic range can be tailored in a wide
range by scaling the dimensions of the MEMS structure
Example: Capacitive pressure sensor
2p
1p
kxAppF =−= )( 12
( )
( ) 4
3
2max
3
42
1316
1613
RdEtp
txEtpRx
ν
ν
−=∆
<
∆−=
“Convenient” measuring range (dynamic range) for a Si sensor with the area 1 mm2 is p = 0.01 bar … 100 barDynamic range limited by nonlinearity and eventually the membrane touching the bottom wafer (=> advantage: tolerance against pressure shocks)
Readout of a capacitive sensor
1. AC readout (i.e., displacement measurement)
∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼
)sin()( 0 tVtV ω=
)sin()()( 0 tIItI ω∆+= )sin(out tV ωG
V 1 MHz, 12/for A 6
)sin( )(For pF1Typically
====
==
AC
ACAC
AC
VCVi
tVtVC
πωµω
ω
Transfer function of the capacitive pressure sensor
0
0.4
0.8
1.2
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6
dxCC
CUi AC
/10
−≈
∆=∆ ω
max/ pp ∆∆
sign
al c
urre
nt ∆
i
2. DC readout (velocity measurement)
Bias the membrane by “constant” charge and measure voltage changes induced by the motion of the membraneVelocity of the diaphragh is measured, NOT positionMotional current (calculate typical example)Examples: microphone, dynamical pressure, vibration, resonators
2p
1p
F = F(t)Ubias
C = C(t)
R
Q= CV = constant over τ = RC
=> ∆V=-Ubias∆C/C
3. Readout using a tuned circuit
IMPROVED RESOLUTION BY TUNING!
Vs RiRloss
CRs
ZC
LRL
MIX LFP
0 deg (I)90 deg (Q)
ref
Q-factor enhancement to the 90 deg signal => high resolutionSqrt(Q) enhancement of the noise at the resonance frequencyLong term stability of the tuned circuit problematic (e.g., T coeff of the inductor)0 deg signal is a measure of the loss factors
Suited particularly for dynamic measurements: dynamic pressure, microphone, vibration, ..
4. Capacitive sensors based on the loss factor measurement
Object to be measured e.g. fingerprint
e.g. matrix of electrodes,of interdigited capacitor
R CC
Vs MIX LFP
0 deg R information90 deg (Q)
ref
5. Resonating capacitive sensors
Advantages over static capacitive sensors
• Improved resolution (at least sometimes)• Easier to make a readout electronics which does not limit the resolution• Output can be coded in the frequency of the output voltage. This may be an advantage.• Several measurements can be measured transformed into a mechanical resonance measurement (strain, force, pressure, acceleration, temperature, mass depostion, ..)• Additional information can be obtained from the dissipation (Q value of the mechanical resonance)
Equation for the mechanical resonance
ηx
m
k
Fext
2
220222
0 )(
1)(
Q
Gωω
ωω
ω
+−
=
ηω /0mQ =
Transfer function at operation point:
00 2 fπω =
extFkxdtdx
dtxdm =++η2
2
Fext = Mechanical force + Electrical force
Motional quantities (“m”)Static capacitance
mBequivn TRkv 4. =
mC
mL
mR0C
.equivmV
.equivnv
mi
Mechanical resonator as a sensor
Spring term: strain, force, pressure, acceleration, ..
Mass term: mass change, pressure, ..
Loss term: pressure from flow loss, viscous surface effects, rapid mass fluctuations, ...
mC
mL
mR0C
.equivmV
.equivnv
mi
Example: resonating pressure sensor (Tomi Mattila et al, 2000)
w=420 µm
L=158 µm
h=5 µm
d=1 µm
Network analyser
Uin
Uout
(a)
(b)
r(µm) 1.0 1.5 2.0 3.0
etch holes
-60
-50
-40
-30
-20
-10
364200 364300 364400 364500Frequency (Hz)
Uou
t/Uin
(dB
)-200
-150
-100
-50
0
50
Phas
e (d
eg)
Example: resonating pressure sensor (2)
CmRm Lm
Cw
Uin
Cp
UDC
50 ΩΩΩΩ
100 nF
100 pFCcoaxCin
25 pF50 ΩΩΩΩ
Uout
0.001 0.01 0.1 1 10p (mbar)
Dam
ping
fact
or r
(Ns/
m) a = 1.0 µµµµm
a = 1.5 µµµµma = 2.0 µµµµma = 3.0 µµµµm
10-5
10-9
10-6
10-7
10-8
Measurement techniques related to capacitive sensors
Dynamical range of AC readout
∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼
)sin()( 0 tVtV ω=
)sin()()( 0 tIItI ω∆+= )sin(out tV ω
n
out
GVV max
best At
G
Background current limits dynamical range
Bridge measurement
∆∆∆∆p ⇒⇒⇒⇒ C →→→→ C+ ∆∆∆∆C ∼∼∼∼
)sin()( 0 tVtV ω=
)sin(out tV ωG
-1
• Zero background signal• Improved dynamical range• Reference C on the same chip!• Stability requirement on the source relieved
• Resolution NOT improved• Inverter should be stable!
Guarding of parasitic capacitances
Intrinsic parasitic C(cannot be bootstrapped)(f.ex. anchor area ofreleased MEMS)
Parasitics from cables, f.ex.(CAN be guarded)
(active) guardingbootstrapping
Guarding of parasitic capacitances (2)
The potential of the signal line is keptat virtual ground => no current flowsacross Cp
Force feedback
∆∆∆∆p ⇒⇒⇒⇒ Vfb→→→→ Vfb + ∆∆∆∆Vfb
∼∼∼∼
)sin(out tV ωG
-1
Electrostatic force
Feedback controller
2
2
2dAVFe
ε=
Features of force feadback
Nonlinearity of the spring does not matter since the membrane is not moving
Linearity requirement now concerns the feedback circuitry, not the transducer
Obtaining linearity requires special solutions since electrostatic force is proportional to the voltage squared
Transfer function is modified by the feedback
Micromechanical silicon precision scale
Exploded view
Electrodes
Contact pad
SpringSOI chip
Glass base
Metallization (Al)
Top view
VTT Automation, VTT Electronics, MIKES
(First) prototype electronics for the precision scale
Ze
Preamplifier
OSC600kHz L P L F
SQRT-1
+1
RF-amplifier
G
PI
Scale
DVM
Reference
0, 1
1
1 0
dC/C
(ppm)
0, 1
1
1 0
dC/C
(ppm)
Brownian Noise of Capacitive Sensors
DYNAMICS OF MEMS CAPACITOR
( ) ( ) nmechn FFVVxd
Akxdtdx
dtxdm +++
−=++ 2
22
2
2εη
mechF is a mechanical force (f.ex., gravity)
nV is the voltage noise )(2)()( τδτ TRktVtV Bnn =+
nF is the force noise )(2)()( τηδτ TktFtF Bnn =+
• Nonlinear dynamics (=> mixing effects)
• Coupling between electrical and mechanical
noise
From friction to noise
Linearized system: ωω ω fGx )(=
Transfer function Qi
kG/
/)(0
220
20
ωωωωωω
+−= ,
mk=0ω
Thermal noise
( ) ( )
hyvyysluku mekaaninenon , in,kitkakerroon
4
42/
21
21
0
2
2
402
02
0
2220
40
2
22
2
2
kTkf
kTk
kQfd
Qkfx
xkTk
Bn
Bn
nn
nB
ωηη
η
ωπω
ωωωωω
=
=
==+−
=
=
∫∞
Brownin liike
(White force noise assumed)
Q=100
Q=10
1,0E-10
1,0E-09
1,0E-08
1,0E-07
1,0E-06
0,1 1 10
√xn2 /d
2 (1
/√H
z)
0/ωω
Q=100
Q=10
Displacement noise
Low-freq noise decreases by increasing Q (= decreasing friction)(vacuum encapsulation)
Mechanical noise
measω
0at 4
at 4/
20
20
22
==
==∆
ωω
ωωω
kdQTk
kdTQk
fdx
B
mBn
Signal-to-noise
-10
-5
0
5
10
0,1 1 10
Q=100
Q=10
( ) ( )
kd
fQd
x ωω
ωωωω
ωω Re//1
/1Re2
022
02
20
2
+−
−=
0/ωωat low frequencies
fTk
Fk
Q
dxdx
NS
B
n
∆=
=
4
//
0
22
ω
dx /Re ω
Other noise sources!
Intrinsic only!
Q=100
Signal-to-noise is the important quantityNot signal itself (i.e. sensitivity)
Capacitive sensor has an internal noise mechanism which arises from internal energy dissipation.
It is temperature dependent.
It can be quantitatively predicted !
Magnitude of the noise can be calculated from the equipartiontheorem ½ kx2 = ½ kBT and the equation of motion for the released membrane of the capacitive sensor.
The latter determines how noise is shaped with frequency.
Electrostatic actuation (the concept of transducer)
Actuation (i.e. movement) of the released electrode by using electrostatic force
x
U=0
U=V
d-x
springel FF = <=> kxxd
AV=
− 2
20
)(2ε
Pull in at 0
2
278
CkdV pi =
The electrodes are snapped together due to the nonlinearity of the electrostatic force
“Eigencurve” of a moving parallel plate capacitor
0
0,2
0,4
0,6
0,8
1
1,2
0 0,2 0,4 0,6 0,8 1
V/V
pi
δV2
δV1
δx/d1 δx/d2
Stabilize this point and measure the voltage
maxmax /or /by controlled / QQiidx ACAC
CV curve of a moving plate capacitor
-8 -6 -4 -2 0 2 4 6 8
4
5
6
7
8
9
C
(pF)
UDC (V)
• CV curve shows that the sensor is working• Can be used for self test
MiscellaneousLiterature1. Stanfordin tämään kevään “Introduction to Sensors” kurssi
http://design.stanford.edu/Courses/me220/me220.html 2. M. Elwenspoek, R. Wiegerink: “Mechanical Microsensors” ,
Springer 2001 (contains no S/N analysis!!!)3. Universal capacitive readout (= general purpose ultra-low noise
CMOS ASIC, contact [email protected])4. Y. Netzer, “The Design of Low-Noise Amplifiers”, Proc. IEEE
Vol. 69, No. 6, p. 728 – 741 (1981).
http://design.stanford.edu/Courses/me220/list.html#notes
Lecture 1: Human/Animal Sensors Lecture 2: Sensor Performance Characteristics Lecture 3: Strain Gauges Lecture 4: Capacitive Sensors and Accelerometer Fundamentals Lecture 5: ADXL50 Micromachine Accelerometer Demonstration Lecture 6: Piezoelectric Sensors Lecture 7: Pressure Sensors Lecture 8: Thermometers Lecture 9: Flow Sensors Lecture 10: Radiation Sensors Lecture 11: IR Sensors Demo: IR Motion Lecture 12: Inductive and Magnetic Sensors Lecture 13: Active Sounding Measurement Techniques ExamplesLecture 14: DC Motor Demonstration Lecture 15: Micromachine Sensor Design and Fabrication Lecture 16: Chemical Sensors
Lecture 17: Gyroscopes
Other (RF) MEMS coursess
• Prof. Antti Räisäsen RF-MEMS kurssi• International master’s program on RFMEMS through the AMICOM
Network of Excellence (Advanced MEMS for communications)• VTT is a partner is this network• Contact persons: [email protected], [email protected]