Transcript Higher Order Sigma-Delta Modulators Interfaces for Capacitive Inertial Sensors Michael Kraft

Higher Order Sigma-Delta
Modulators Interfaces for
Capacitive Inertial Sensors
Michael Kraft
Yufeng Dong
Nano-Scale Systems Integration Group
School of Electronics and Computer Science
Southampton University
Overview
Electrostatic Force Feedback for Capacitive Sensors
Second Order SDM Approach
Higher Order SDM Interfaces
Theory
Simulation
Measurement Results
Conclusions
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Electrostatic Force Feedback (1/2)
Electrode
Pyrex capping wafer
Suspension system
Silicon proof mass
Movable proof mass
Sensing element can be for a accelerometer,
gyroscope, pressure sensor, microphone, force
sensor….
Capacitors are easy to realize in MEMS
They can be used for sensing AND actuation
Michael Kraft
Yufeng Dong
Ref.:
Analog Devices, ADXL05
Fixed electrodes
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Electrostatic Force Feedback (2/2)
Advantages, closed loop approach
accuracy beyond manufacturing tolerance
better bandwidth, dynamic range, linearity
small proof mass motion reduces nonlinear effects
inherent to MEMS sensors
damping, unwanted electrostatic forces, suspension
Advantages, digital closed loop approach
direct digital sensor  DSP, “smart sensor”
improved stability, no electrostatic pull-in
‘noiseshaping’ in the signal band
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Nonlinear Effects in MEMS Sensors
Differential change in capacitance is only
proportional to displacement for small proof mass
motion
Damping mechanism is based on squeeze film
effects, only for small proof mass motion, the
damping constant can be assumed as constant
Suspension system can be assumed as linear only
for small proof mass motion
Electrostatic force due to electrical excitation signals
can be neglected only for small proof mass motion
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Second Order SDM Interface
fs
S/H
Pickoff
1
C(z)
Compensator
0
Comparator
Digital
bitstream
V out
Vf
Vf
Digital control based on sigma-delta modulation (SDM)
System determined by feedback network (for high gain)
Feedback in form of quantized force pulses
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
SDM Force Feedback
Mainly applied to micromachined accelerometer
Limited work for gyroscopes and pressure sensors
Lewis, C.P., Hesketh, T.G., Kraft, M. and Florescu, M. A digital pressure transducer. Trans.
Inst. of Meas. and Control, Vol 20, No. 2. pp. 98-102, 1998.
Little commercial exploitation
More suitable for medium to high performance sensors
State of the Art (until very recently):
Sensing element used as loop filter
Very low dc gain of the mechanical integrator functions
Only second order noise shaping
Relatively poor Signal to Quantisation Noise Ratio (SQNR)
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Early Examples
Henrion, W., Disanza, L., Ip, M., Terry, S. and Jerman, H. Wide dynamic range direct digital
accelerometer. IEEE Solid State Sensor and Actuator Workshop, pp. 153-157, Hilton Head
Island, 1990.
Yun, W., Howe, R. T. and Gray, P. Surface micromachined, digitally force-balanced
accelerometer with integrated CMOS detection circuitry. IEEE Solid-State Sensor and Actuator
Workshop, pp. 126 - 131, Hilton Head Island, 1992.
De Coulon, Y., Smith, T., Hermann, J., Chevroulet, M. and Rudolf, F. Design and test of a
precision servoaccelerometer with digital output. 7th Int. Conf. Solid-State Sensors and
Actuators (Transducer '93), Yokohama, pp. 832 - 835, 1993.
Smith, T., Nys, O., Chevroulet, M., De Coulon, Y. and Degrauwe, M. Electro-mechanical
sigma-delta converter for acceleration measurements. IEEE International Solid-State Circuits
Conference, San Francisco, pp. 160-161, 1994.
Smith, T.; Nys, O.; Chevroulet, M.; DeCoulon, Y.; Degrauwe, M. A 15 b electromechanical
sigma-delta converter for acceleration measurements. IEEE International Solid-State Circuits
Conference, 41st ISSCC., pp. 160-161, 1994.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Smith et.al., 1994
Smith, T.; Nys, O.; Chevroulet, M.; DeCoulon, Y.; Degrauwe, M.; A 15 b electromechanical
sigma-delta converter for acceleration measurements. IEEE International Solid-State Circuits
Conference, 41st ISSCC., pp. 160-161, 1994.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
End of 90’ties Examples
Spineanu, A., Benabes, P. and Kielbasa, R. A piezoelectric accelerometer with sigma-delta
servo technique. Sensors and Actuators, A60, pp. 127-133, 1997.
Kraft, M., Lewis, C.P. and Hesketh, T.G. Closed loop silicon accelerometers. IEE
Proceedings - Circuits, Devices and Systems, Vol. 145, No. 5, pp. 325 – 331, 1998.
Boser, B. E. and Howe, R. T. Surface micromachined accelerometers. IEEE J. of Solid-State
Circuits, Vol. 31, No. 3, pp. 336-375, 1996.
Lemkin, M.A. Micro accelerometer design with digital feedback control. University of
California, Berkeley, Ph.D. dissertation, 1997.
Lemkin, M.A and Boser, B. A Three-axis micromachined accelerometer with a CMOS
position-sense interface and digital offset-trim electronics. IEEE J. of Solid-State Circuits, Vol.
34, No. 4, pp. 456-468, 1999.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Kraft and Lewis, 1996
Top electrode
Seism ic mass
}
}
C1
Bottom electrode
x
C2
5mm
A bulk micromachined accelerometer with capacitive signal pick-off.
Theoretical prediction of limit cycle modes
Established framework for system level modelling and simulation
Comparison between analogue and digital force-feedback
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Kraft and Lewis, 1996
Simulink model for parameter optimization
10
0
-10 0
10
1
10
2
fc = 56Hz 10
0
-20
Open loop and closed frequency response.
Open loop cut-off frequency 56Hz
Closed loop:~300Hz
-40
-60
-80
0
10
Michael Kraft
Yufeng Dong
1
10
Frequency [Hz]
2
10
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Lemkin and Boser, 1999
Multi-axis Position Sensing
Interface
•
x-axis
PROOFMASS
SENSE
CAPS
Vstep
y-axis
SHIELD
3-axes device
Fully integrated
Surface-micromachined
Michael Kraft
Yufeng Dong
z-axis
Cref
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Lemkin and Boser, 1999
Prototype Die Photo
•
ain
m
S
sensor
x/V
2 - z -1
1-bit ADC
lead
compensator
comparator
Fel
double
integration
position
sense
V/Fel
1-bit DAC
electrostatic
actuation
Block diagram as before, sensing element
only provides noise-shaping
Sampling frequency 500kHz
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Lemkin and Boser, 1999
Parameter
Proof Mass [mg]
Natural Frequency [kHz]
Sense Capacitors [fF]
Noise Floor [mG/rt-Hz]
Dynamic Range [dB]
Bandwidth [Hz]
Full Scale [G]
Michael Kraft
Yufeng Dong
x-axis
0.38
3.2
101
0.11
84
100
+/-11
y-axis
0.26
4.2
78
0.16
81
100
+/-11
z-axis
0.39
8.3
322
0.99
70
100
+/-5.5
Higher Order SDM Interfaces for Capacitive Inertial Sensors
MEMS SDM Gyroscope
Sense combs
4.5mm
Drive
Circuitry SE2
SE 2
Drive
Circuitry SE1
SD
y
Z
X
700m m
Sensing Sensing
Element 1 Element 2
Circuitry
Feedback electrodes
Digital Control Signal Circuitry
Drive combs
Main Features:
• Digital closed loop control in
the sense mode
Xuesong, J., Wang, F., Kraft, M., and Boser, B.E. An integrated surface
micromachined capacitive lateral accelerometer with 2 uG/rt-Hz resolution.
Tech. Digest of Solid State Sensor and Actuator Workshop, pp. 202-205,
Hilton Head Island, USA, June 2002.
Michael Kraft
Yufeng Dong
• Low voltage parallel plate drive
based on charge control
Higher Order SDM Interfaces for Capacitive Inertial Sensors
MEMS SDM Gyroscope
Quadrature
Cancellation
Sensing Mode Control
fs=1MHz
VQC
Position
Sense
Position
Sense
Compensation
AGC
Control
Frequency
Tuning
Low-pass SDM in the sense
mode
Charge
Control
Circuitry
PLL
Drive Mode Control
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
MEMS SDM Gyroscope
Sensing Mode Control
fs=1MHz
Position
Sense
Sense electrodes
Compensation
Feedback electrodes
Low-pass SDM in the sense
mode
Drive Mode Control
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Analysis of 2nd Order SDM Loop
Linearize: - assume small deflection of the proof mass
- replace one bit quantiser with gain KQ and added white noise
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Analysis of 2nd Order SDM Loop
Electrostatic force on proof mass:
1
Fel  sgn D 
Small signal feedback gain:
1  AV
kF   o 2 f
2 d0
o A Vf 2
2 d 0  sgn D  x 2
2
s  z1
s  p1
Simplest compensator, lead-lag:
C s  
Signal transfer function:
k x k C k Q C s 
Yout
 STF 
2
FI
ms  bs  k  k x kC kQ k F C s 
ms 2  bs  k
 NTF 
FI
ms 2  bs  k  k x k C k Q k F C s 
NQ
Quantisation noise transfer function:
STF is flat in the signal band of interest, therefore the signal is allowed to pass through unchanged
The NTF has low gain in the signal band and higher gain for higher frequencies above the signal
band → ‘noise-shaping’
The low-frequency gain of the sensing element, equal to the inverse of the spring constant,
determines the noise shaping characteristics. High low-frequency gain means high quantisation
noise suppression in the signal band. For a purely electronic SDM modulator the low-frequency gain
is very high, as the loop filter consists of (near-) ideal integrators resulting in much better noise
shaping characteristics. This means that a SDM with a micromachined sensing element can never
reach the noise shaping characteristics of a second order, purely electronic SDM.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Analysis of 2nd Order SDM Loop
Bode Magnitude Diagram of the STF
2
80
0
70
-2
Magnitude (dB)
Magnitude (dB)
90
60
50
-4
-6
40
-8
30
-10
20 2
10
3
4
10
10
-12 2
10
5
10
Bode Magnitude Diagram of the NTF
3
4
10
10
5
10
Frequency (rad/sec)
Frequency (rad/sec)
Left: Magnitude plot of the signal transfer function.
Right: magnitude plot of the noise transfer function.
Procedure to calculate the SQNR:
PSD of white sampled noise as introduced by the 1 bit quantiser:
PSD at the output of the digital sensor:
N Q2,out  E 2 ( f ) NTF
2
E 2 ( f )  eRMS
2
fs
with eRMS 
q
12
2
B
Total in-band noise given by: n02   NQ2 ,out df
0
Signal-to-quantisation-noise-ratio is given by:
Michael Kraft
Yufeng Dong
 RMS of input signal 

SQNR  20 log 
n02


Higher Order SDM Interfaces for Capacitive Inertial Sensors
Analysis of 2nd Order SDM Loop
0
0.5*((A*e0*0.5*V_amp^2)/((d0-u[1])^2)-(A*e0*0.5*V_amp^2)/((d0+u[1])^2))
-20
DC component of electrostic force due to excitation voltage
Input acceleration signal
-40
Mass-Spring-Dashpot,
limited displacement
Sum
e0*A*(2*u[1]/(d0^2-u[1]^2))
v v elocity
Deflection -> diff. Capacitance
a acceleration
deltaC
kc
Pick-off
s+zero_comp
V
s+pole_comp
Compensator
delta_out
S/H
Comparator
To Workspace
Sample
and Hold1
PSD [dB]
Fext
Input
acceleration
-60
Sampling
clock
x displacement
-80
-100
-120
-140
Sw itch
t_sim
Clock
Vfb
-0.5*e0*A*(u[1]^2/(d0+u[2])^2)
Feedback Voltage
Electrostatic Force
if Bottom Plate is Energized1
x[32n]
x[2n]
ydec
Comb Filter
FIR
Decimation
To Workspace3
Mux2
To Workspace1
-160
-180
-200
0.5*e0*A*(u[1]^2/(d0-u[2])^2)
Dec. output
Electrostatic Force
if Top Plate is Energized1
0
1
2
3
4
Frequency [Hz]
5
4
x 10
0
-20
PSD [dB]
Simulink model of the digital accelerometer
-40
SNR = 57.4dB @ OSR=50
-60
Rbit = 9.25 bits @ OSR=50
-80
-100
-120
-140
Linear analysis only valid to a certain point
For more detailed studies and stability analysis
use system level simulation
Consideration of second order effects possible
Michael Kraft
Yufeng Dong
-160
-180
-200
0
500
1000
1500
2000
2500
3000
3500
4000
Frequency [Hz]
Power spectral density of the output
bitstream for an input acceleration signal
of 1G and a frequency of 100Hz.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Analysis of 2nd Order SDM Loop
140
SNR [dB]
130
120
No noise
110
Elec. noise only
100
90
Brow n noise only
80
Brow n noise and
elec. noise
70
60
50
0
500
1000
1500
2000
Oversampling ratio M
Linearised mathematical model of the closed loop sensor with all noise sources.
SNR as a function of the oversampling ratio.
NTFQN ( s ) 
DOUT ( s )
Quantisation noise transfer function:
V ( s)
Other noise sources need to be considered as well
Brownian noise: adds directly to the input signal
Brownian noise transfer function:
NTFBN ( s ) 
2
QN

DOUT ( s )
F
2
BN
( s)
1
1

1  K Fb M ( s ) K xc K PO C ( s ) K q K Fb M ( s ) K xc K POC ( s ) K q

M ( s ) K xc K POC ( s) K q
1 K Fb M ( s ) K xc K POC ( s) K q
LF

1
K Fb
Electronic noise from the capacitive position measurement interface
Electronic noise transfer function: NTF ( s)  DOUT ( s) 
EN
2
V PO ( s )
Michael Kraft
Yufeng Dong
K POC ( s ) K q
1  K Fb M ( s ) K xc K POC ( s) K q

1
K Fb M ( s ) K xc
Higher Order SDM Interfaces for Capacitive Inertial Sensors
2500
Issues with
nd
2
Order SDM Loop
Sensing element only determines the noise-shaping
High dependency on fabrication tolerances
At best second order noise-shaping can be achieved
No noise shaping of electronic noise introduced by pick-off
circuits
Limited low-frequency gain
Only way to increase the signal-to-quantisation-noise ratio is
to increase the sampling frequency
High requirements for interface and control circuits
High sampling rates lead to higher electronic noise
Second order SDM exhibit limit cycles which give rise to
dead-zones
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Higher Order SDM Approach
Use similar architectures to electronic SDM A/D
converters for MEMS capacitive sensors
Higher SQNR and SNR at lower sampling frequencies
Noise-shaping determined by sensing element plus
electronic filter
Small proof mass motion alleviates nonlinear effects
Noise shaping of electronic noise possible
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Higher-order SDM Topology
Input-referred
Electronic Noise
Brownian Noise
Input
Sensing
Element
Quantization Noise
Electronic
Filters
Pickoff
Electrostatic Force
Conversation
K
Quantizer
A
D
F
V
Challenges:
No access to internal nodes of sensing element
Electronic gain constants have to be optimised for stability and performance
High tolerances of the mechanical sensing element parameters
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Example: Higher-order (5th order)
SDM for an Accelerometer
Three additional integrators to form a fifth order
electro-mechanical SDM control system
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Comparison: 2nd, 3rd, 4th and 5th ΣΔM
Quantisation Noise Transfer Functions for 2nd, 3rd, 4th and 5th order SDM loops
The higher the order the better the quantisation noise suppression in the signal
band
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Output Spectrum - Simulation
OSR=256
Noise floor considerably reduced in the signal band
Simulation considers only quantisation noise
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Prototype Board
PCB Prototype in
SMD technology
Fully differential
design
Possible to switch
between 2nd, 3rd,
4th, 5th order SDM
architectures
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Hardware Implementation
Diode
Envelope
Demodulator
Fullydifferential
Instrument
Amplifier
Quantizer
3-stage
Distributed Feedback
Fully-differential
Continuous-time
Integrator Network
S5
S6
S7
One-bit
D/A
Sampling Clock fs
Bitstream
S1
S2
S3
S4
S5
S6
S7
Sampling Clock fs
Clock Switch Control Sequencies
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
Second Order loop – sensing element only as loop filter
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
Third order loop – sensing element + 1 electronic
integrator as loop filter
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
Forth order loop – sensing element + 2 electronic
integrators as loop filter
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
Fifth order loop – sensing element + 3 electronic integrators as
loop filter
noise floor of -100dB --- compared to -50dB for 2nd order loop
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Measurement vs Simulation
No input signal
Input signal, 1kHz, 0.5G
Very good agreement between measurement and simulation
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Transfer Functions of a 5th Order SDM (1)
Brownian Noise:
NTFBN ( s ) 
DOUT ( s )
F
2
BN
( s)
LF
1

K Fb
Quantisation Noise:
NTFQN ( s ) 
DOUT ( s )
V
2
QN
( s)
LF
Michael Kraft
Yufeng Dong

1 3
(
)
sTs
K F1
K PO K1 K 2 K 3 K q  [ K Fb M ( s ) LF K xc 
]
K POC ( s )
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Transfer Functions of a 5th Order SDM (2)
Electronic Noise from Pickoff Stage:
NTFPO ( s ) 
DOUT ( s )
V
2
PO
( s)
LF

1
K F1
K Fb M ( s ) LF K xc 
K POC ( s )
Electronic noise of the pickoff circuit in a higher order
electromechanical ΣΔM system may be further reduced depending on
the value of the two terms in the denominator if the following
condition applies:
K Fb M ( s ) LF K xc 
Michael Kraft
Yufeng Dong
K F1
K POC ( s )
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Feedback Nonlinearity
The electrostatic feedback force on the proof mass is given by:
Ffb  sgn( Dout )
 0 AfbV fb
2
2( d 0  sgn( Dout )  x )
2
 F0
1
(1  sgn( Dout )
x
)
2
d0
… and is not constant but depends on the residual proof
mass motion, x
Force variations during
feedback pulses
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Without Feedback Linearization (1)
Ain
Dout
Hn
High Order
Electronic
Integrator
Ffb  sgn( DOUT )
 0 AfbV fb2
2( d 0  sgn( DOUT ) x )2
 sgn( DOUT ) F0 [1  sgn( DOUT )2(
x
d0
KQ
Quantizer
)  3(
1
x
d0
)  4(
2
x
)  ...]
3
d0
F0   0 AfbV fb2 / 2d02
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Without Feedback Linearization (2)
The high order harmonics in
the electrostatic feedback force.
Michael Kraft
Yufeng Dong
The third harmonic in the SDM spectrum
of the output bitstream.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
With Feedback Linearization (1)
Ain
Dout
Hn
High Order
Electronic
Integrator
KQ
Quantizer
V fb*  V fb  sgn( DOUT )  l
l  ( x / d 0 )V fb
Michael Kraft
Yufeng Dong
F  sgn( DOUT ) F0
*
fb
Higher Order SDM Interfaces for Capacitive Inertial Sensors
With Feedback Linearization (2)
SDM spectrum of the output bitstream
with a linear feedback DAC.
Michael Kraft
Yufeng Dong
SDM spectrum of the output bitstream
with a linear feedback DAC and
a nonlinear pickoff interface.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Other Higher Order SDM Topologies(1)
5th-order Distributed Feedback with resonators (DFBR) Electromechanical SDM.
6th-order Distributed Feedback with resonators (DFBR) Electromechanical SDM.
5th-order Distributed Feedback and Feedforward (DFFF) Electromechanical SDM.
Other Higher Order SDM Topologies(2)
Feedforward with resonator (FFR)
An under-damped sensing element needs a phase compensator to stabilize the loop.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Sensitivity Analysis on
Fabrication Tolerances
A Monte Carlo analysis is performed for the sensing element and the coefficients of electronic
integrators using the deviation of +/-5% for mass, +/-20% for damping, +/-20% for spring
stiffness, and +/-2% for coefficients of electronic integrators.
Feedforward with resonator (FFR)
Michael Kraft
Yufeng Dong
Distributed Feedback with resonator (DFBR)
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope with Higher Order SDM
Vibratory rate gyroscope –
Simulink model
5th-order lowpass SDM
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope 5th-order lowpass SDM
The bode diagram of the transfer
functions of the signal, quantisation noise
and electronic noise.
Michael Kraft
Yufeng Dong
Output bitstream spectrum of the lowpass Σ∆M interface with local amplification
around signal bandwidth.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Petkov and Boser, 2005
The fourth-order interface achieved a resolution of 1
/s/ √Hz with a gyroscope to an input rotation rate of
25 /s at 20 Hz and
150μg/√Hz with an accelerometer measured over
100-Hz signal band with a 1-g dc input.
V. P. Petkov and B. E. Boser, "A Fourth-Order Interface for Micromachined Inertial Sensors",
IEEE Journal of Solid-state Circuits, Vol. 40, NO. 8, pp. 1602-1609, Aug. 2005.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope 8th-order Bandpass SDM(1)
An 8th order band-pass SDM interface with the topology of distributed
feedback
with resonators (DFBR) constituting the sense block
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope 8th-order Bandpass SDM(2)
The bode diagram of the transfer
functions of the signal, quantisation noise
and electronic noise in DFR.
Michael Kraft
Yufeng Dong
Output bitstream spectrum of the
bandpass Σ∆M interface in DFR.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope 8th-order Bandpass SDM(3)
An 8th order band-pass Σ∆ interface with the topology of feedforward
with resonators (FFR), constituting the sense block
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Gyroscope 8th-order Bandpass SDM(4)
The bode diagram of the transfer
functions of the signal, quantisation noise
and electronic noise in FFR.
Michael Kraft
Yufeng Dong
Output bitstream spectrum of the
bandpass Σ∆ interface in FFR.
Higher Order SDM Interfaces for Capacitive Inertial Sensors
References / Bibliography
V. P. Petkov and B. E. Boser, A Fourth-Order Interface for Micromachined Inertial Sensors,
IEEE Journal of Solid-state Circuits, Vol. 40, No. 8, pp. 1602-1609, Aug. 2005.
T. Kajita, U.K. Moon, and G. C. Temes, A Two-Chip Interface for a MEMS Accelerometer, IEEE
Transactions on Instrumentation and Measurement, Vol. 51, No. 4, August 2002, pp. 853-858.
Dong, Y., Kraft, M. and Gollasch, C.O, A high performance accelerometer with fifth order sigma delta
modulator. J. Micromech. Microeng. Vol. 15, pp. S22-S29, 2005.
Dong, Y., Kraft, M. and Redman-White, W. Force feedback linearization for higher-order electromechanical
sigma delta modulators. Proc. MME 2005 Conference, pp. 215-218, Belgium, Sept. 2005.
Dong, Y., Kraft, M. and Redman-White, W. Noise analysis for high-order electro-mechanical sigma-delta
modulators. Proc. 5th Conf. on Advanced A/D and D/A Conversion Techniques and their Applications
(ADDA), pp. 147-152, Limerick, Ireland, July 2005.
Dong, Y., Kraft, M. and Redman-White, W. High order bandpass sigma-delta interfaces for vibratory
gyroscopes. Proc. 5th IEEE Sensors, Irvine, USA, Nov. 2005.
Dong, Y., Kraft, M. and Redman-White, W. High order noise shaping filters for high performance inertial
sensors. To be appear in IEEE Trans. on Instrumentation and Measurement, Nov. 2007.
Dong, Y., Kraft, M., Hedenstierna, N. and Redman-White, W. Microgyroscope control system using a highorder band-pass continuous-time sigma-delta modulator. Proc. Transducers 2007 Conference, Vol. 2, pp.
2533-2536, France, June 2007.
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors
Conclusions
Established a theoretical framework for application of higher
order SDM control systems to capacitive MEMS sensors
Implemented a hardware realisation to verify the principle
Higher order SDM can improve the performance of existing
MEMS sensing elements by:
Small proof mass motion
Shaping the (quantization) noise at low OSR
Linearization of the feedback
Substantial improvements to existing capacitive MEMS
sensors such accelerometers, gyroscopes, pressure sensors,
microphones, force sensors
Focus on the ‘E’ and ‘S’ in MEMS as a route for future
innovations for MEMS
Michael Kraft
Yufeng Dong
Higher Order SDM Interfaces for Capacitive Inertial Sensors