Higher Order SigmaDelta Modulators Interfaces for Capacitive Inertial Sensors

1
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
2
Overview

• Electrostatic Force Feedback for Capacitive
  Sensors
• Second Order SDM Approach
• Higher Order SDM Interfaces
• Theory
• Simulation
• Measurement Results
• Conclusions

3
Electrostatic Force Feedback (1/2)

• 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

4
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

5
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

6
Second Order SDM Interface

• Digital control based on sigma-delta modulation
  (SDM)
• System determined by feedback network (for high
  gain)
• Feedback in form of quantized force pulses

7
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)

8
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.

9
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.

10
End of 90ties 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.

11
Kraft and Lewis, 1996

• Theoretical prediction of limit cycle modes
• Established framework for system level modelling
  and simulation
• Comparison between analogue and digital
  force-feedback

12
Kraft and Lewis, 1996
Simulink model for parameter optimization
Open loop and closed frequency response. Open
loop cut-off frequency 56Hz Closed loop300Hz
13
Lemkin and Boser, 1999

• Multi-axis Position Sensing Interface

• 3-axes device
• Fully integrated
• Surface-micromachined

14
Lemkin and Boser, 1999

• Prototype Die Photo

Block diagram as before, sensing element only
provides noise-shaping

• Sampling frequency 500kHz

15
Lemkin and Boser, 1999
16
MEMS SDM Gyroscope
Sense combs
Feedback electrodes
Drive combs

• Main Features
• Digital closed loop control in the sense mode
• Low voltage parallel plate drive based on charge
  control

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.
17
MEMS SDM Gyroscope
Quadrature Cancellation
Sensing Mode Control
f
1MHz
s
VQC
Position
Compen-
Sense
sation
AGC
Position
Control
Sense
Charge
Frequency
Control
Tuning
Circuitry

• Low-pass SDM in the sense mode

PLL
Drive Mode Control
18
MEMS SDM Gyroscope
Sensing Mode Control
f
1MHz
s
Position
Compen-
Sense
sation
Sense electrodes
Feedback electrodes

• Low-pass SDM in the sense mode

Drive Mode Control
19
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
20
Analysis of 2nd Order SDM Loop
Electrostatic force on proof mass Small
signal feedback gain Simplest compensator,
lead-lag Signal transfer function Quantisati
on 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.

21
Analysis of 2nd Order SDM Loop
Procedure to calculate the SQNR PSD of white
sampled noise as introduced by the 1 bit
quantiser with PSD at the output of the
digital sensor Total in-band noise given
by Signal-to-quantisation-noise-ratio is given
by
22
Analysis of 2nd Order SDM Loop

• 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

23
Analysis of 2nd Order SDM Loop
Linearised mathematical model of the closed loop
sensor with all noise sources.
SNR as a function of the oversampling ratio.

• Quantisation noise transfer function
• Other noise sources need to be considered as well
• Brownian noise adds directly to the input signal
• Brownian noise transfer function
• Electronic noise from the capacitive position
  measurement interface
• Electronic noise transfer function

24
Issues with 2nd 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-no
  ise 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

25
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

26
Higher-order SDM Topology
Input-referred Electronic Noise
Brownian Noise
Quantization Noise
Sensing Element
Input
Electronic Filters
K
Pickoff
Quantizer
Electrostatic Force Conversation
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

27
Example Higher-order (5th order)SDM for an
Accelerometer

• Three additional integrators to form a fifth
  order electro-mechanical SDM control system

28
Comparison 2nd, 3rd, 4th and 5th S?M

• 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

29
Output Spectrum - Simulation

• OSR256
• Noise floor considerably reduced in the signal
  band
• Simulation considers only quantisation noise

30
Prototype Board

• PCB Prototype in SMD technology
• Fully differential design
• Possible to switch between 2nd, 3rd, 4th, 5th
  order SDM architectures

31
Hardware Implementation
32
Second Order loop sensing element only as loop
filter
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
33
Third order loop sensing element 1 electronic
integrator as loop filter
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
34
Forth order loop sensing element 2 electronic
integrators as loop filter
Measurement Results
No input signal
Input signal, 1kHz, 0.5G
35
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

36
Measurement vs Simulation
No input signal
Input signal, 1kHz, 0.5G

• Very good agreement between measurement and
  simulation

37
Transfer Functions of a 5th Order SDM (1)
Brownian Noise
Quantisation Noise
38
Transfer Functions of a 5th Order SDM (2)
Electronic Noise from Pickoff Stage
Electronic noise of the pickoff circuit in a
higher order electromechanical S?M system may be
further reduced depending on the value of the two
terms in the denominator if the following
condition applies
39
Feedback Nonlinearity

• The electrostatic feedback force on the proof
  mass is given by

• and is not constant but depends on the residual
  proof mass motion, x

Force variations during feedback pulses
40
Without Feedback Linearization (1)
41
Without Feedback Linearization (2)
The third harmonic in the SDM spectrum of the
output bitstream.
The high order harmonics in the electrostatic
feedback force.
42
With Feedback Linearization (1)
43
With Feedback Linearization (2)
SDM spectrum of the output bitstream with a
linear feedback DAC and a nonlinear pickoff
interface.
SDM spectrum of the output bitstream with a
linear feedback DAC.
44
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.
45
Other Higher Order SDM Topologies(2)
Feedforward with resonator (FFR)
An under-damped sensing element needs a phase
compensator to stabilize the loop.
46
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)
Distributed Feedback with resonator (DFBR)
47
Gyroscope with Higher Order SDM
Vibratory rate gyroscope Simulink model
5th-order lowpass SDM
48
Gyroscope 5th-order lowpass SDM
The bode diagram of the transfer functions of the
signal, quantisation noise and electronic noise.
Output bitstream spectrum of the low-pass S?M
interface with local amplification around signal
bandwidth.
49
Petkov and Boser, 2005
Low pass
The fourth-order interface achieved a resolution
of 1 /s/ vHz with a gyroscope to an input
rotation rate of 25 /s at 20 Hz and 150µg/vHz
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.
50
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
51
Gyroscope 8th-order Bandpass SDM(2)
The bode diagram of the transfer functions of
the signal, quantisation noise and electronic
noise in DFR.
Output bitstream spectrum of the bandpass S?M
interface in DFR.
52
Gyroscope 8th-order Bandpass SDM(3)
An 8th order band-pass S? interface with the
topology of feedforward with resonators (FFR),
constituting the sense block
53
Gyroscope 8th-order Bandpass SDM(4)

The bode diagram of the transfer functions of
the signal, quantisation noise and electronic
noise in FFR.
Output bitstream spectrum of the bandpass S?
interface in FFR.

54
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 high-order band-pass continuous-time
  sigma-delta modulator. Proc. Transducers 2007
  Conference, Vol. 2, pp. 2533-2536, France, June
  2007.

55
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