High Performance Inertial

Navigation Grade Sigma-Delta

MEMS AccelerometerP. Zwahlen, Y. Dong, A-M. Nguyen, F.Rudolf, Colibrys SA

P. Ullah, V. Ragot, Sagem

September 18th 2012

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Why a MEMS accelerometer for high end applications ?

� MEMS accelerometers are widely spread in the automotive, consumer

and industrial markets

� MEMS accelerometers are starting to replace established, expensive

and fragile high-end electromechanical devices

� MEMS accelerometers can offer same or better performance at lower

cost, lower power consumption, smaller size and greater strength

� Some MEMS accelerometers have already penetrated on civilian and

defence programs (Airbus and Boeing aircrafts, gun lauched smart

munitions, *)

� MEMS accelerometers will soon be compatible with high-end inertial navigation systems

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Objectives

AIDA: a MEMS accelerometer for inertial navigation

� Need

– Lower cost compared to non-MEMS solutions

– High performance� Full scale ~15g

� Bias stability < 1mg

� Rectification < 10 µg/g²

� Scale factor < 1000 ppm

� Bandwidth > 300 Hz

� Low frequency noise ~1 µg/√Hz (equivalent to 18bit resolution for 300Hz bandwidth)

� Architecture

– Bulk silicon pendular MEMS� Robust, stable

– Capacitive sense/actuation� Detector == actuator

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Accelerometer architecture

� Open-loop limitations

– Noise� Brownian noise due to gas damping

– Linearity� Squeeze-film effect, electrostatic forces (non-linear functions of gap)� Vibration-induced rectification

– Bandwidth� Limited by natural frequency and damping

� Closed-loop solution

– Noise� Operation at high Q for the MEMS possible. Allows reduction of Brownian noise� Position control achieved through electronic regulation

– Linearity� Reduced seismic mass excursion thanks to feedback control. Improved vibration rectification

– Bandwidth� Signal bandwidth extension up to over 10kHz � Precise data time stamp is essential for inertial navigation and guidance applications

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Part I: System Description

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Closed-loop sensor System Architecture

� Capacitive bulk micromachined MEMS Chip

� Capacitive position detector including low resolution ADC (7 bit

equivalent)

� Digital loop filter (position control)

� Oversampled Sigma-Delta converter

– Pulse density modulation

– 1-bit comparator � Bitstream output

– 1-bit DAC applying constant voltage to bottom or top electrode

� Acceleration mean value estimated through high linearity 1-bit DAC

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Sigma-Delta converter for accelerometer

Sigma-Delta principle

� High frequency 1-bit conversion instead of high resolution

� High quantization noise rejected in high frequency by noise shaping

concept

� High linearity achieved by averaging

Low passband noise

Increased computing

complexity

Hardware simplicity

(analog detection,

actuation voltage)

High sampling frequencyHigh linearity

Linearization of

electrostatic forces

Trade-offsAdvantages( )

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2

0

2

2

1

e

VAFe

ref

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MEMS sensor and detection

MEMS Sensor

� 3-stack silicon electrode assembly

� High temperature Silicon Fusion Bonding

(SFB) technology resulting in highly

stable assembly

� Time multiplexing concept

– Allows usage of same electrodes for both sense readout and forcing

Capacitive detection

� Voltage amplifier topology

� Analog modulation / demodulation

(Correlated Double Sampling)

� Switched capacitor

– Chosen for its versatility to interface with different size MEMS capacitors

– Dedicated phase for charge injection removal

Mass

SpringTop electrode

Bottom electrode

Middle electrode

Mass

SpringTop electrode

Bottom electrode

Middle electrode

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Testboard V2 Accelerometer interface

Sigma-Delta board V2

� Test board

– FPGA for digital filtering, decimation & control sequencing

– Clock oscillator– Power supply decoupling capacitors– Communication interface

� ASIC & MEMS & Temp sensor packaged inside a standard JLCC-44 package

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System design for high stability

� High stability MEMS sensor

– Careful spring anchoring design

– 3-stack Silicon MEMS technology with Silicon Fusion Bonding technologies for excellent long-term stability and hermeticity

– Die attach stress decoupling technique

� Detection chain offset reduction

– CDS technique

– Charge injection removal

� High stability voltage reference

– Low impedance output up to high frequency

– Low noise

– High stability

� Matching and repeatability of electrode switching operation

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Part II: Performance Results

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Noise Transfer Function

CIC filtered output

Bitstream output

� White noise: 1µµµµg/sqrt(Hz)

� Noise bandwidth: 300 Hz

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Temperature modeling Bias (K0)

� Bias temperature

slope: Class 200 µµµµg/°C

� Low bias residues:

– < 300µg

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Temperature modeling Bias (K0): Statistical distribution

� Statistical evaluation over a population of 11 boards

– all components are based on a single MEMS design and technology

� Thermal bias

slopes

distribution is

below 150 µµµµg/°C

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Temperature modeling Scale Factor (K1)

� Excellent Scale

Factor

repeatability

(device to device)

� Scale factor

temperature slope:

Class 100 ppm/°C

� Low scale factor

residues:

– < 200 ppm

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Temperature modeling Scale Factor: Statistical distribution

� Scale factor temperature slope distribution below 100 ppm/°C

� Scale factor residues distribution: < 200 ppm

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Temperature modeling Misalignment (Kp)

� Misalignment

temperature slope:

< 50 µµµµrad/°C

� Misalignment

residues:

– < 60 µrad

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Temperature modeling Misalignment: Statistical distribution

� Misalignment temperature slope distribution: < 50 µµµµrad/°C

� Misalignment residues distribution: < 60 µµµµrad

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Short-term bias stability under warm-up

� Controlled within +/-10 µµµµg

under warm-up condition

with a 10g FS sensor

– � 1 ppm bias stability

� Limited warm-up transient

left after thermal

compensation

� Warm-up potential after low-

pass filtering over 160s &

time derivation

– 8µg/mn (obtained over a larger sample)

– Compliant with gyrocompass alignment requirements

data averaged over 1s

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Bias stability / Allan variance

� 10 sec of data observation is

enough to get micro-g signal

precision

� Signal stability is guaranteed at

observation time of at least up

to 300 sec

external vibrations noises

Bias instability (Random flicker noise)

Bias stability: Temporal, Allan Variance, PSD

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Vibrations: 2nd order non-linearity (K2)

Non-linearity (K2)

� K2(f) device to device

repeatability

� K2 < 10 µµµµg/g2 (0 to 100 Hz)

� K2 < 20 µµµµg/g2 (up to 1 kHz)

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Performance review

g4000Shock resistance

[0; 100] Hz / [100; 1000] Hzµµµµg/g210 / 20Vibration (K2)

mW100Power consumption

After 3rd order polynomial curve fittingµµµµrad60Kp residues

After 3rd order polynomial curve fittingppm200K1 residues

ppm/°C100K1 Temperature slope

Scale Factor (K1)

µµµµrad/°C

µµµµg

µµµµg/°C

µg/mn

µµµµg/√√√√Hz

g

Unit

50Kp Temperature slope

Misalignment (Kp)

After 3rd order polynomial curve fitting300Temperature residues

max150Temperature bias slope

8Short-term (under warm-up)

Bias stability (K0)

typ.1Noise

typ.15Full scale range

CommentValue

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Conclusions

� The combination of MEMS pendular and sigma/delta allows "medium

navigation grade" class performances with gyrocompass functions.

– Bias stability� 8 µg/min bias stability under warm-up condition

� 300 µg of residues

– Scale factor� 200 ppm residues

� MEMS based accelerometer highlights

– High shock tolerance

– Low weight

– Size

– Cost (Batch manufacturing process)

� The next developments will focus on packaging and system integration.

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Thank you for your attention