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Silicon Resonant Accelerometer for Inertial Navigation Systems
Yong Ping XUYong Ping XUDept of Electrical and Computer EngineeringDept of Electrical and Computer Engineering
National University of SingaporeNational University of Singapore
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Outline Introduction The proposed silicon resonant
accelerometers Sense resonator Circuit chip design Measurement results Conclusion
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IntroductionShortcomings of global positioning
system (GPS) It is subject to signal jamming It cannot be used indoor GPS has low update rate and is
therefore not suitable for high-speed tracking
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Introduction (cont.)
Inertial navigation system (INS) INS employs inertial sensors (accelerometer
and gyroscope) to track the position and orientation of an object.
An INS is a self-contained system. Once the initial position is known, it can track the object without the need of any reference.
It can be used when GPS is not available It can also used as a complement to the GPS
system
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Inertial navigation system Stable platform INS
King, A.D., “Inertial navigation – Forty Years Evolution”, GEC Review, Vol.13, No.3, 1998, pp.140-149
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Inertial navigation system (cont.)
King, A.D., “Inertial navigation – Forty Years Evolution”, GEC Review, Vol.13, No.3, 1998, pp.140-149
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Inertial navigation system (cont.)
Due to the nature of integration, INS requires the accelerometer to have low bias error
∫ ∫Acceleration
GlobalAccel
VelocityPosition
Bias errors
2)(
2
0 0
tddts b
t t
b εττε == ∫ ∫
Position error (due to a constant bias error, εb)
εb = 0.01g
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Sources of bias errors DC bias
Output offset of the accelerometer when the acceleration is zero.
Random/white noise Originated from thermal noise, both mechanical and
electrical Flicker noise
Device flicker noise and offset in readout circuit Temperature
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Bias stability Bias stability
Bias change over a specified period of time, typically around 100 seconds, at zero acceleration.
Bias stability is usually measured by Root Allan Variance floor
Bias stability is usually specified as 1σ value with a unit of mg/hr (milligravityper hour)
Typical requirement for inertial navigation is < 100 µg
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Displacement sensing silicon accelerometers Displacement sensing
The acceleration is measured by the displacement of the proof mass
The displacement can be detected by optical, capacitive, piezoresistive tunneling principles
Amini, B.V., et al., “A 4.5-mW closed loop DS micor-gravity CMOS SOI accelerometer,” IEEE JSSC, pp.2983-2991,Dec 2006
ak
m
k
Fx
−=
−=
a – Accelerationm – Massk – Spring constant
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Resonant silicon accelerometer
Advantage: Radiation resistant Axially loaded, allowing large dynamic range Quasi digital output Potential to achieve good bias stability
aSFfPSff ⋅+≅⋅+= 00 1
Force sensing
P – Axial force applied a - Accelerationfo – resonant frequency at zero acceleration
f – frequency of oscillation under accelerationSF – Scaling factor (Hz/g)
EILS 22 π=
Hopkins, R.E., et al., “The Silicon Oscillating Accelerometer,” Draper Laboratory, MA, USA
Where: ∆f
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The proposed silicon resonant accelerometer
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Block diagram of one channel
Oscillator core Amplitude controlSense resonator
Differentiator differentiates the position signal ∆Cs, to make the feedback force in phase with the velocity of the resonator beam
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Challenges in readout circuits Low phase noise in the close-in (carrier) region
Flicker and thermal noise MEMS resonator nonlinearity
Low noise interface circuit Low polarization voltage requires sensitive interface
circuit Extremely small capacitance change (0.5–20fPF) to be
sensed Nonlinearity of MEMS resonator
Low noise amplitude control Parasitic feed-through in MEMS resonator
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SOI sense resonator
Cross sectionAcceleration axial
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Differential resonator
Double-ended tuning fork(single-ended operation)
Modified for differential operation
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Measred frequency response
127,600 127,650 127,700 127,750 127,800-50
-45
-40
-35
-30
-25
-20
frequency (Hz)
Gai
n (d
B)
Vp=25VQ=30000
Vp = 25VQ = 30,[email protected]
127,380 127,430 127,480 127,530 127,560-50
-45
-40
-35
-30
frequency (Hz)
gain
(dB
)
Vp=3.3V
Vp = 3.3VNo resonant peak can be seendue to parasitic feed-through
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Readout circuit chip design Low noise capacitive sensing interface Offset free differentiator Amplitude control circuits
CHS peak detector and error amplifier VGA and buffer
Driving scheme with separate sense and driving phase to avoid feedthrough
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Low noise capacitive sensing interface
Cp1=700fFCp2=400fF
f0= 135kHzfs = 5MHz
Clear Autozero Sense Drive
igpsT
LH
H
sT
T
i
s
s
CCCCCwhere
zCC
C
C
C
CC
C
C
V
zC
zV
+++=
+⋅⋅
+⋅=
∆− 21
2
10
)(
)(
Transfer function:
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Operations in four phasesClear phase Autozero phase
Sense phase Drive phase
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Main features of the sensing interface Two step CDS (error stored in CA and CB) Fast-settling OTA Compensation resistor Rc to improve the settling time
Capacitive isolation, Cc, during drive phase
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Amplitude control scheme
- Amplitude control is to set the oscillator amplitude to a desired value (VR0) to maximize the SNR, while keep the oscillator from the nonlinear region, since the nonlinearity causes large close-in phase noise, hence poor bias stability.
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CHS peak detector and error amplifier
Vx
vdm
Vx
ovV)12( −ovV)12( −−0
ovTicmx VVVV −−=
I0
Vicm ± Vdm
ovTdmicmxovdm
ovTicmxdm
VVVVVVVFor
VVVVVFor
2,)12(
),12(0
−−+=−≥
−−=−<≤
VT – transistor threshold voltageVov – Overdrive voltage (VGS – VT)
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Complete chip
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Measurement results
SOI sense resonators and proof mass Circuit chip
- SOI MEMS process from MEMSCAP- 0.35 CMOS process from AMS Tested @1.25mbar
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Frequency readings
Output waveform from VGA Frequency reading after a PLL,multiplied by 420.
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Scale factor measurement
-1 0 1127.5
127.55
127.6
127.65
127.7ch
ann
el 1
ou
tpu
t (k
Hz)
Acceleration input (g)-1 0 1
129
129.05
129.1
129.15
129.2
chan
nel
2 o
utp
ut
(kH
z)
Scale factor ≈ 145 (Hz/g)
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Measured Allan variance
Root AVAR (0.4 mHz)
Bias stability:
Root AVAR/Scale factor = 0.4 mHz/145 Hz/g ≈ 2.9 µg
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Summary
Parameter Unit Value
Technology Sense resonator SOI MEMS
Readout chip 0.35µm CMOS
Resonant frequency kHz ~ 127
Polarization voltage V 3.3-6.4
Supply voltage V 3.3
Scale factor Hz/g ~ 145
Bias stability µg ~ 3
Resolution µg/sqrt(Hz) 20
Power dissipation mW 23
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Comparison
Comparison with previous resonant accelerometer
[1] T. A. Roessig et al., "Surface-micromachined resonant accelerometer," in Transducers’97, June 1997, pp. 859-862.
3µg
[1]
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Comparison (cont.)
Comparison with previous capacitive accelerometer
[2] M. Lemkin and B.E. Boser, "A three-axis micromachined accelerometer with a CMOS position-sense interface and digital offset-trim electronics," in IEEE J. Solid-State Circuits, vol. 34, pp. 456-468, Apr. 1999.[3] H. Luo, et al. “A post-CMOS micromachined lateral accelerometer,” in J. of MEMS, Vol. 11, No. 3, pp. 188-195, June, 2002.[4] J. Chae, H. Kulah, and K. Najafi, “A monolithic three-axis micro-g micromachined silicon capacitive accelerometer,” in J. of MEMS, Vol.14, No. 2, pp. 235-242, Apr. 2005
[2]
[3]
[4]
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Conclusion
A high performance silicon resonant accelerometer with CMOS readout circuit has been demonstrated
The accelerometer, operating under 3.3V, achieves 3µg bias stability and 20µg/Hz1/2 resolution in 1Hz offset
The good performance is made possible by Differential MEMS resonator Low noise capacitive sensing interface Effective amplitude control scheme and low noise implementation Chopper stabilized rectifier and error amplifier Separate sensing and driving phase High and CMOS compatible Polarization voltage through charge
pump The accelerometer is suitable for high-precision INS
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Acknowledgements Dr Lin He,
Shanghai Institute of Microsystem and Information Technology, China
Dr Moorthi Palaniapan Dept of Electrical and Computer Engineering,
National University of Singapore
Thank you!
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Mechanical leverage
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Allan Variance
Allan variance is a function of averaging time Originally proposed and used for characterize the clock systems
( )∑−
=+ −
−=
1
1
21 )()(
)1(2
1)(
n
iii yy
nAVAR τττ
Allan Variance:
y – average value of the measurement in bin i,τ– averaging timen – total number of bins
τt
τ τ τ τ
n x τ