新加坡国立大学硅共振加速度计

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

CMOS ET 2009 Vancouver 2

Outline Introduction The proposed silicon resonant

accelerometers Sense resonator Circuit chip design Measurement results Conclusion


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


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


Inertial navigation system Stable platform INS

King, A.D., “Inertial navigation – Forty Years Evolution”, GEC Review, Vol.13, No.3, 1998, pp.140-149


Inertial navigation system (cont.)

King, A.D., “Inertial navigation – Forty Years Evolution”, GEC Review, Vol.13, No.3, 1998, pp.140-149


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


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


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


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


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


The proposed silicon resonant accelerometer


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


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


SOI sense resonator

Cross sectionAcceleration axial


Differential resonator

Double-ended tuning fork(single-ended operation)

Modified for differential operation


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


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


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:


Operations in four phasesClear phase Autozero phase

Sense phase Drive phase


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


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.


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)


Complete chip


Measurement results

SOI sense resonators and proof mass Circuit chip

- SOI MEMS process from MEMSCAP- 0.35 CMOS process from AMS Tested @1.25mbar


Frequency readings

Output waveform from VGA Frequency reading after a PLL,multiplied by 420.


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)


Measured Allan variance

Root AVAR (0.4 mHz)

Bias stability:

Root AVAR/Scale factor = 0.4 mHz/145 Hz/g ≈ 2.9 µg


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


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]


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]


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


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!


Mechanical leverage


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

新加坡国立大学 硅共振加速度计

Engineering

Transcript of 新加坡国立大学 硅共振加速度计

新加坡国立大学硅共振加速度计

Transcript of 新加坡国立大学硅共振加速度计