Silicon Resonant Accelerometer for Inertial Navigation Systems

1
Silicon Resonant Accelerometer for Inertial
Navigation Systems

• Yong Ping XU
• Dept of Electrical and Computer Engineering
• National University of Singapore

2
Outline

• Introduction
• The proposed silicon resonant accelerometers
• Sense resonator
• Circuit chip design
• Measurement results
• Conclusion

3
Introduction

• Shortcomings 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

4
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

5
Inertial navigation system

• Stable platform INS

King, A.D., Inertial navigation Forty Years
Evolution, GEC Review, Vol.13, No.3, 1998,
pp.140-149
6
Inertial navigation system (cont.)
King, A.D., Inertial navigation Forty Years
Evolution, GEC Review, Vol.13, No.3, 1998,
pp.140-149
7
Inertial navigation system (cont.)
Global Accel
Acceleration
Position
Velocity
Bias errors
Position error (due to a constant bias error, eb)
eb 0.01g
Due to the nature of integration, INS requires
the accelerometer to have low bias error
8
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

9
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 1s value
  with a unit of mg/hr (milligravityper hour)
• Typical requirement for inertial navigation is lt
  100 mg

10
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

a Acceleration m Mass k Spring constant
Amini, B.V., et al., A 4.5-mW closed loop DS
micor-gravity CMOS SOI accelerometer, IEEE JSSC,
pp.2983-2991,Dec 2006
11
Resonant silicon accelerometer
Force sensing
Df
Where
P Axial force applied a - Acceleration fo
resonant frequency at zero acceleration f
frequency of oscillation under acceleration SF
Scaling factor (Hz/g)
Hopkins, R.E., et al., The Silicon Oscillating
Accelerometer, Draper Laboratory, MA, USA

• Advantage
• Radiation resistant
• Axially loaded, allowing large dynamic range
• Quasi digital output
• Potential to achieve good bias stability

12
The proposed silicon resonant accelerometer
13
Block diagram of one channel
Oscillator core
Sense resonator
Amplitude control

• Differentiator differentiates the position signal
  DCs, to make the feedback force in phase with the
  velocity of the resonator beam

14
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 (0.520fPF) to
  be sensed
• Nonlinearity of MEMS resonator
• Low noise amplitude control
• Parasitic feed-through in MEMS resonator

15
SOI sense resonator
Cross section
Acceleration axial

16
Differential resonator
Double-ended tuning fork (single-ended operation)
Modified for differential operation
17
Measred frequency response
Vp 25V Q 30,000_at_0.1mbar
Vp 3.3V No resonant peak can be seen due to
parasitic feed-through
18
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

19
Low noise capacitive sensing interface
Cp1700fF Cp2400fF f0 135kHz fs 5MHz
Transfer function
20
Operations in four phases
Autozero phase
Clear phase
Sense phase
Drive phase
21
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

22
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.

23
CHS peak detector and error amplifier
Vicm Vdm
I0
Vx
VT transistor threshold voltage Vov Overdrive
voltage (VGS VT)
24
Complete chip
25
Measurement results
SOI sense resonators and proof mass
Circuit chip

• SOI MEMS process from MEMSCAP
• 0.35 CMOS process from AMS

Tested _at_1.25mbar
26
Frequency readings
Output waveform from VGA
Frequency reading after a PLL, multiplied by 420.
27
Scale factor measurement
Scale factor 145 (Hz/g)
28
Measured Allan variance
Root AVAR (0.4 mHz)
Bias stability Root AVAR/Scale factor 0.4
mHz/145 Hz/g 2.9 mg
29
Summary
30
Comparison
Comparison with previous resonant accelerometer
1
3mg
1 T. A. Roessig et al., "Surface-micromachined
resonant accelerometer," in Transducers97, June
1997, pp. 859-862.
31
Comparison (cont.)
Comparison with previous capacitive accelerometer
2
3
4
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
32
Conclusion

• A high performance silicon resonant accelerometer
  with CMOS readout circuit has been demonstrated
• The accelerometer, operating under 3.3V, achieves
  3mg bias stability and 20mg/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

33
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

34
Thank you!
35
Mechanical leverage
36
Allan Variance
Allan Variance

• y average value of the measurement in bin i,
• averaging time
• n total number of bins

t
t
t
t
t
t
n x t

• Allan variance is a function of averaging time
• Originally proposed and used for characterize the
  clock systems