ee180d systems design sensor systems 1

Networked Embedded System Design EE180D Lecture 2

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EE1 8 0D : S E N S O R S Y S T E M S - I

L E C T U R E 2

T A B L E O F C O N T E N T S

1. SENSOR TECHNOLOGY AND EMBEDDED SYSTEMS ............................................................................ 2 2. SENSOR SYSTEM OVERVIEW ....................................................................................................................... 2 3. SENSOR SYSTEM STANDARD FIGURES OF MERIT ............................................................................... 6 4. SENSOR PERFORMANCE LIMITATIONS EXAMPLE: ACCELEROMETER SENSOR DRIFT ........ 7 5. INERTIAL SENSORS: ACCELEROMETER SENSOR EXAMPLE ........................................................... 9

First Generation Single Axis Accelerometer ......................................................................................................... 9 Current Generation Triaxial Sensor System ......................................................................................................... 9

6. CAPACITIVE POSITION SENSOR ............................................................................................................... 13 7. ACCELEROMETER SENSITIVITY EXAMPLE ......................................................................................... 15 8. ROTATION AND ROTATION RATE SENSORS: THE RATE GYROSCOPE ....................................... 17

Rate Gyroscope Operating Principles ................................................................................................................ 17 Rate Gyroscope Drift-Induced Errors ................................................................................................................ 19 Surface Micromachined microgyroscope ............................................................................................................ 21 First Generation Single Axis Rate Gyroscope ..................................................................................................... 22 Triaxial Rate Gyroscope ...................................................................................................................................... 23 Rate Gyroscope Performance: Responsivity scaling .......................................................................................... 27

9. MEMS MICROGYROSCOPE OFFSET, OFFSET DRIFT, TEMPERATURE COEFFICIENT AND NOISE ......................................................................................................................................................................... 29 10. FREQUENCY-DEPENDENT AND SAMPLING BANDWIDTH-DEPENDENT SENSITIVITY ......... 30 11. NOISE SOURCES ............................................................................................................................................ 33 12. SENSOR PERFORMANCE LIMITATIONS EXAMPLE: ACCCELEROMETER ............................... 38 13. SENSOR SAMPLING AND ENERGY REQUIREMENTS ........................................................................ 42 14. SENSOR ENERGY REQUIREMENTS ........................................................................................................ 44 15. SEISMIC SENSOR CASE STUDY ................................................................................................................ 45 16. POLYMER RESISTIVE PRESSURE SENSORS ........................................................................................ 47 17. OPTICAL BIOMEDICAL SENSOR SYSTEMS ......................................................................................... 47


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1 . SENSOR TECHNOLOGY AND EMBEDDED SYSTEMS

• Sensor systems are primary components of embedded systems

o Often, the need for control and the required use of sensors motivates the product requirements for embedded systems

§ Industrial § Automotive § Infrastructure monitoring and control

o Also, as the cost of sensor systems has reduced (as the result of microelectromechanical

systems (MEMS) progress), sensors now appear in consumer products § Cellular phone systems § Personal devices § Entertainment systems § Future Wireless Health devices

• Sensor systems requirements may heavily constrain the design of hardware and software systems

§ Data acquisition requirements § Energy requirements § Signal processing requirements

2 . SENSOR SYSTEM OVERVIEW

• The ideal, simplified sensing system

• Physical signal provided by a source propagates through a signal channel to the sensor system

• transducer receives the input physical signal (that may have acquired superimposed noise and suffered distortion in the channel for a non-ideal application).

• transducer converts received physical signal into an electronically observable signal.

physical signal

at source

Signal

ChannelTransducer

Analog Signal

Processing

Analog-to-Digital

Data Conversion

physical signal

at transducer

Digital Signal

Processing

output signal

physical signal

at source

Signal

ChannelTransducer

Analog Signal

Processing

Analog-to-Digital

Data Conversion

physical signal

at transducer

Digital Signal

Processing

output signal


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o example, a change in temperature may be converted into a change of resistance if the transducer is a temperature-sensitive resistor

o acceleration signal may result in the motion of a transducer proof mass resulting in a displacement and a change in electronic capacitance

o light intensity signal may be converted into an electronic current by a photodiode detector.

• analog signal processing interface

o detects the electronically observable transducer output and conditions signal

o analog-to-digital converter stage

o samples the analog signal and presents this to an appropriate (and optional) digital signal processing stage

• Critical filtering step and strategies

o In the ideal case, sampling fidelity is achieved for signals at frequencies below the Nyquist rate

o Nyquist sampling theorem applies to band limited signal at frequency fc

§ Nyquist sample rate at 2fC

• Many sampling rate issues to consider

o Spectral range of input signal may not be known at design time

o Design strategy for variable sampling rate

§ Tunable analog filters that track sampling rate

• Complex, expensive components, calibration requirement, high energy dissipation

§ Preferred approach

• Front end high frequency anti-aliasing filter set at maximum expected sample frequency Nyquist rate

o Follow with digital sampling and filtering to obtain proper rate.

• Sampling rate and noise

o Sampling rate selection, when combined with proper filter produces varying sampling bandwidth over which noise spectral density is integrated

o Typical example: integrated noise amplitude increases as square root of bandwidth


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o Note that resolution for monitoring a signal will depend on sample rate

o Many challenges exist where the combination of performance of sensor, analog and digital systems do not permit achieving a needed resolution level.

• First, the input physical signal is emitted by the source and propagates through the channel.

• The sensor signal channel contributes a distortion in the frequency domain and may also exhibit nonlinear amplitude dependence in extreme examples (although most channels display linear response to the characteristically small signals that are available to sensors).

• Noise signals present at the site of the source also contribute to the input signals and these also propagate through channels that convey noise to the transducer input. It is important to note that noise and signal will be indistinguishable at the sensor input.

o noise signals that arise from the physical environment are not to be considered as sensor limitations and are to be maintained separate from evaluation of sensor systems.

physical signal

at source

Signal

Channel

Distortion

TransducerAnalog Signal

Processing

Analog -to-Digital

Data Conversion+

Digital Signal

Processing

output signal

noise signal(s )

Noise

Channel(s )

+

transducer

input -referred noise

+

transducer

interference signals

(cross -talk)

Combined

Distortion

+

quantization

noise

physical signal

at transducer

+

analog interface


Signals Sensor System

physical signal

at source

Signal

Channel

Distortion

TransducerAnalog Signal

Processing

Analog -to-Digital

Data Conversion+

Digital Signal

Processing

output signal

noise signal(s )

Noise

Channel(s )

+

transducer


+

transducer

interference signals

(cross -talk)

Combined

Distortion

+

quantization

noise

physical signal

at transducer

+

analog interface


Signals Sensor System


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• Specifically, the ENS system designer must be allowed to compute a response from the sensor system given knowledge of an input physical signal amplitude.

o If environmental noise is present as a result of application characteristics, then this will be recorded along with signal.

• It is then the task of subsequent sensor data and information processing to separate source signals.

• Now, sensor noise leads us to a separate discussion that also contributes to some aspects of calibration, however

• The most important noise source to be considered next is that of the transducer itself. Specifically, all transducers display a noise associated with their operation.

o Thus, even in the limit of a noise free environment, the transducer output is finite.

o As we will see, this noise source is observed to be equivalent to some signal and this will lead to the definition of a noise-equivalent signal level for each sensor.

• Continuing to the next source of input noise the role of interference (so-called cross-talk) is encountered.

o Here, the transducer system is presented with signals derived from the input physical signal of interest (for example an atmospheric pressure signal) and temperature variations that create an interfering signal is indistinguishable from the desired signal yet arises from entirely separate phenomena.

o Finally, the analog signal processing interface also contributes an important noise source

o This noise may result from the input-referred noise of the input transistor stages of the analog signal processing system.


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3 . SENSOR SYSTEM STANDARD FIGURES OF MERIT

• The design and operation of sensor platforms relies on the availability of standard definitions for

comparison of sensor systems.

• sensor systems are characterized by means to avoid the impact of environmental noise, channel distortion, or cross-talk.

• The first primary sensor characteristic figure of merit is responsivity, ( a transfer function) the ratio of output signal amplitude to input physical signal amplitude.

�

responsivity =output signal electronic amplitude

input physical signal amplitude

o Often, responsivity is incorrectly applied as a measure of sensor performance

• Sensitivity determines the frequency dependent and measurement bandwidth dependent resolution

of a complete sensing system.

o Obtained by removing all sensor system inputs and measuring the resulting output signal

o output signal results only from noise originating from the transducer itself or signal processing section.

o Since noise at the output is indistinguishable from that produced by an input signal, and

since responsivity is known or can be determined, then the value of the input-referred noise level may be computed

o This is literally the value of input signal that if applied at the input would result in the

observed noise level. • Sensitivity is often referred to as a noise equivalent signal.

�

sensitivity =output signal electronic amplitude in the absence of an input signal

responsivity

o frequency dependence of sensitivity must be considered since noise signal sources are

distributed in frequency.

o low frequency limit of operation encounters the phenomenon of “drift”, a slowly changing value of sensor output, due to low frequency noise sources.

o At high frequency, a broad band, frequency-independent noise region appears due to broad

band noise at the analog signal processing interface.


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o ENS designer must include this frequency dependence along with knowledge of desired signal frequency spectra in computation of sensor system performance.

o Next step: we will illustrate example of a typical accelerometer then consider noise sources

o Demonstrate that fundamental thermodynamic noise sources actually limit performance of

automotive collision sensors for airbag deployment.

4 . SENSOR PERFORMANCE L IMITAT IONS EXAM PLE: ACCELEROMETER SENSOR DRIFT

• The combination of accelerometer and gyroscope systems offers a capability for inertial navigation.

• Specifically, an inertial measurement unit (IMU) may provide rotation information with respect to an inertial reference frame, and acceleration.

• These data combined, can enable orientation of the accelerometer axes to be known. Then, double integration of the accelerometer output can yield absolute position of the IMU in space.

• Clearly, this would have immense applicability in vehicle control, wireless health, personal localization systems, and many others.

• However, fundamental “drift” that appears as a low frequency noise contribution, prevents accurate inertial navigation.

o As an example, a drift in the output of a sensor may appear as an offset signal (a near static value of acceleration that appears in the absence of a physical acceleration input).

• The figure below shows the integrated position error resulting from an acceleration offset signal – demonstrating that small offsets lead to large error in current applications


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• Consider typical error tolerances for an accelerometer with 1000 micro-g offset

o Personal navigation

§ 0.5m accuracy time limit is 10s

§ 50m accuracy time limit is 100s

o Vehicle navigation

§ 50m accuracy time limit is 100s

§ 5 km accuracy time limit is 1000s


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5 . INERTIAL SENSORS: ACCELEROM ETER SENSOR EXAMPLE

• Acceleration sensors (accelerometers) are basic components

o biomedical motion sensing

o seismic measuring stations

o airbag control systems

o manufacturing process control

o inertial navigation systems

o orientation with respect to true vertical

FIRST GENERATION SINGLE AXIS ACCELEROMETER

• The Analog Devices ADXL50 is shown below (at left) with the ADXL02 sensor element at right.

CURRENT GENERATION TRIAXIAL SENSOR SYSTEM


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• Triaxial Accelerometer STMicroelectronics LIS331DLH Accelerometer as used in iPhone platform


11

• Triaxial Accelerometer STMicroelectronics LIS331DLH Accelerometer as used in iPhone platform:

Detail View

• Note Suspension Spring • Note Proof Mass

• Note Capacitor Sensor Displacement electrodes


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• We will compute first responsivity

• Silicon micromachined accelerometer

o proof mass, m,

o monolithic silicon suspension with spring constant, k,

o quality factor, Q

o resonant frequency, ωo =

�

k m .

o acceleration, a = d2Z/dt2, where Z is the coordinate of the package relative to an inertial frame of reference.

o D will be the coordinate of the mass relative to the package

§ D = 0 corresponding to the rest position of the proof mass at zero spring deflection

§ D > 0 downward deflection, D < 0 upward deflection

o Mass position relative to the inertial frame will be Z - D

o Damping will be proportional to the velocity of the mass relative to the package.

§ Damping force = dDbdt

o The forces associated with the spring and damping must equal the force required to accelerate the proof mass, so

or

Proof Mass Suspension

dD

Z

Inertial Reference Frame


dD

Z

Inertial Reference Frame

2

2

( )d Z D dDm kD b

dt dt

−= +

2 2

2 2

d Z d D dDm m b kDdt dt dt

= + +


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o The package acceleration relation to proof mass motion is

�

a =d2D

dt2

+ω0

Q

dD

dt+ ω

0

2D

o where,

• The deflection of the proof mass due to acceleration a(ω), is

.

• This displacement serves as the signal, since it is what will be eventually converted into an electronic signal. The responsivity (signal divided by excitement) of the accelerometer is defined by

• The responsivity expression simplifies for an acceleration signal frequency much less than ωo. In this case,

�

δD = a /ω0

2 and

�

δD /a =1/ω0

2

6 . CAPACITIVE POSITION SENSOR

§ Capacitive position sensors measure variation in displacement current due to change in capacitor gap.

§ Fundamental to pressure, humidity, and many other sensor systems

§ Capacitive plates can be used to directly measure the gap value, δD.

0m

bQ

ω=

( ) ( )2 2

( )( )

O O

aD

j Q

ωω

ω ω ω ω=

− +

( ) ( )2 22 2 2

1

O O

D

a Qω ω ω ω

=− +

Capacitance 2Suspension

_

D1

_

D2

Capacitance 1

Capacitance 2Suspension

_

D1

_

D2

Capacitance 1


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§ This method shows high-resolution measurement capability, but, requires differential measurement architectures to ensure linearity and low drift.

§ contrast to piezoresistive/piezoelectric methods one may design the system with independent control

of position sensor sensitivity and structure compliance.

§ Thus in both the accelerometer and gyro examples resonant frequency of the proof mass system can be made independent of position measurement.

§ scaling issue

o reduction in capacitance area with decreasing sensor scale results in reduction of capacitor

displacement current, thus producing reduced responsivity and reduced sensitivity. o For conventional (large scale) capacitive detectors, 10-4 Å/

�

Hz sensitivity has been demonstrated

§ pressure sensors § accelerometers § seismometers.

§ A capacitance bridge provides position measurement capability. This makes use of a switched capacitor drive, which modulates the desired signal away from dc, reducing 1/f noise.

§ In such systems, sensitivity (noise) is determined by the measurement front end.

§ Further, the feedback system results in an output always at null, eliminating gain errors. Additionally, the force rebalance output is immune to oscillator amplitude and phase drift.

o The resolution is defined by the ratio of the drive voltage to the amplifier front end noise.

Resolutions approaching 106 have been demonstrated

o Stray capacitance to the substrate may limit applicability of capacitive position sensor, in general requiring careful attention to structural design.

Phase Sensitive

Detector

Output

Amplifier

ac coupled

gain stage

output signal

V+

V-

Switched

Capacitor

Drive

Switched

Capacitor

Drive

t

t

Phase Sensitive

Detector

Output

Amplifier

ac coupled

gain stage

output signal

V+

V-

Switched

Capacitor

Drive

Switched

Capacitor

Drive

t

t


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7 . ACCELEROMETER SENSIT IVITY EXAM PLE

• Sensitivity is critical for

o Determining maximum achievable resolution

o Determining the length of time required for a sensor system to achieve a given level of resolution

• System impact includes energy demand associated with sampling time

• We will examine both transducer noise sources and electronic signal processing system noise sources

• Transducer noise sources

o Thermal drift is a particularly significant source of error. Typical accelerometer applications require that output be integrated twice (once to obtain velocity, and a second time to obtain position).

o Small bias errors will thus translate into large motion/position errors.

§ For example, a 10 µg bias error yields a 0.6 km/hour motion error.

o Sources of thermal drift include

§ linear expansion coefficient of the silicon suspension (10-5/K)

§ temperature dependence of the spring constant of suspension, k (10-4/K)

§ package thermal expansion (resulting in position sensor drift).

o Thermomechanical noise contributes an additional source

• Thermo-mechanical noise provides a fundamental limit for sub-milli-g sensitivity microaccelerometer development.

• For an ideal accelerometer, the limitation on mass reduction arises from thermally-induced mass motion.

• The thermal noise (formal analog of Johnson noise for a resistor) arises from the equipartition theorem.

o Specifically, absent any external influence, the total energy in each axis of oscillation mode of a system (for example the spring mass device) is equal to kBT/2.


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o The rms value of mass position, Drms, for all frequencies, is then computed from

�

1

2kδD

rms

2=1

2kBT

• As an example of the magnitude of Drms, for a mass suspension of spring constant k = 1N/m, the rms mass motion δDrms ≈ 0.6Å (orders larger than desired signal!).

• The value of mass motion over a narrow frequency bandwidth is frequency dependent and depends on Q. The rms value of δD, induced by the thermomechanical force, FT, is determined from the frequency dependent δD value

�

δDT =FT

M ωO

2−ω

2( ) + j ωOω( ) Q( )

• The integral of (1/2)|δDT|2 over all frequencies determines the value of FT. The frequency dependent mass motion in a 1Hz bandwidth is,

�

δDT =4kTωO

MQ ωO

2−ω

2( )2

+ ωOω( )2

Q2( )

• Note that the mass motion induced by acceleration of the mass suspension, a, (the accelerometer “case” or “package”) and the accelerometer responsivity, given above, have the same frequency dependence. Thus, the thermal noise equivalent acceleration (TNEA), the ratio of these signals is frequency independent

�

TNEA ≡4kTωO

MQ

• It is useful to consider how important this may be

o We will analyze an automotive collision impact microsensor example and observe that this noise represents an important sensitivity limitation for this application.

• Must first consider what portion of an input spectrum an instrument measures

o First consider power spectral density


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8 . ROTATION AND ROTATION RATE SENSORS: THE RATE GYROSCOPE

• Gyroscope Applications

o Wide application for controlling orientation of vehicles and machinery

o Primary and critical component of inertial navigation systems

o Automotive applications for yaw rate sensor

§ Braking control

• Conventional rotating mass gyroscope

o Direct measurement of orientation in space

o Typical air-bearing support/vacuum drive/feedback controlled gimbals/rotation transducer output for gimbals

o Innovations by Sperry in 1930’s

• Sensitivity

o Characterized as a precession rate in degrees/sec

o Navigation-capable systems must be 10-3 - 10-6 degrees/sec.

• Oscillatory rate gyroscope

o Method discovered in 1890

o Direct measurement of rotation rate (contrast with orientation sensor)

o Biological system examples

• Advantages

o No rotating (wearing) components

o Short start-up time

o Compact, low-power

o Potential for high-performance

o Demonstrated MEMS rate gyroscopes implemented in micromachines silicon structures

• Disadvantages

o Reduced sensitivity

o Increased drift

RATE GYROSCOPE OPERATING PRINCIPLES

• Rate Gyroscope converts rotation rate into a displacement. that may be measured directly, using the Coriolis Force.

• The Coriolis Force is an apparent force observed in a rotating reference frame that appears to act on moving objects.


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• An Ideal Rotation Rate Transducer may be implemented using the Coriolis Force principle.

• The Coriolis force operates on moving masses and is harmonic with drive frequency

• The rate gyroscope system will carry two masses (m) supported on structure having vertical

restoring forces of k, quality factor Q, resonance frequency, ωd. Masses supported at radius R with motion along the x-axis of

trRrdA

ωsin1

+=

trRrdA

ωsin2

−−=

• Masses are, therefore, being driven at the resonance frequency of the vertical suspension. This provides the greatest natural amplification of out-of-plane Coriolis force-induced motion.

V

_

V

_

V

_

Harmonic

Coriolis

Deflection

Harmonic

Horizontal Mass

Motion


Harmonic

Coriolis

Deflection

Harmonic

Horizontal Mass

Motion


rA

rA

R

rA

rA

R


19

Alternatively, the masses could be supported on a separate structure having a torsional resonance at ωd

• Coriolis force on each mass is

Ω×= mVFC

2

• where Ω is rotation and V is velocity of mass

• Consider Z-axis out of page, X-axis along line of motion, Y-axis vertical direction on drawing. For the case of rotation about the Z axis, the deflection of the mass by the Coriolis force is

tmrFddAC

ωω cos2 Ω=

• The deflection of the mass in the y-direction (in-plane) is

tQrm

QF

k

QFy d

d

A

d

CC ωωω

δ cos2)(2 ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Ω===

• Deflection is enhanced by driving the oscillator system at its resonance with a gain of Q.

• For Earth rate = 4.17 x 10-3 degrees/sec = 7.3 x 10-5 rad/sec, rm = 10µ, Q = 103,

ωd = 104 rad/sec,

δyC = 1.46 x 10-10 m

• Response within the detection range of high-stability capacitance measurement systems.

• Small deflection response introduces error for devices operating with high 1/f noise. The application of feedback bridge methods will be critical.

• Conclusion : ideal rate gyro concept should meet inertial navigation requirements with substantial margin.

• Bias errors and output drift, limiting sensitivity, must arise from non-ideal operation - focus of current development.

RATE GYROSCOPE DRIFT-INDUCED ERRORS

• The use of a rate gyroscope for measuring the orientation of an object encounters error.

• Since the rate gyroscope measures rotation rate (rather than orientation) then orientation is obtained by sampling the output of the rate gyroscope and integrating the rate gyroscope output with respect to time, once.


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• Of course, this means that the origin of orientation is not known

• Also, small offset errors in rate measurement are integrated and lead to an accumulation of error.

• The figure below shows the integrated position error resulting from a rotation rate offset signal – demonstrating that small offsets lead to large error in current applications

• Consider typical error tolerances for a rate gyroscope with a 1 milli-degree/second offset

o Personal navigation

§ 1 degree accuracy time limit is 1000s

§ 10 degree accuracy time limit is 100s


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SURFACE MICROMACHINED MICROGYROSCOPE

• Design Goals

o High responsivity

o Low thermal noise

o Large signal capacitance structures

o High Q

o Mode matching

o Low resonance frequency

• Design Challenges

o Achieving low resonance frequency

o Achieving low damping and high Q.

o Material properties

o Gas film damping

o Mode matching

o Drift

• Solutions:

o Feedback control

• Current Implementation:

o Microelectromechanical Systems (MEMS) principles

o How are forces generated?

• Example first generation microgyroscope


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FIRST GENERATION SINGLE AXIS RATE GYROSCOPE

From A Symmetrical and Decoupled Microgyroscope with electroforming process on insulating substrate” Alper, S.E., Akin, T., Proceedings of The 16th European Conference on Solid-State Transducers, September 15-18, 2002


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TRIAXIAL RATE GYROSCOPE

• Triaxial Rate Gyroscope Proof Mass, Actuator, and Sense Structures for the STMicroelectronics L3G4200D Top View


24

• Triaxial Rate Gyroscope Proof Mass, Actuator, and Sense Structures for the STMicroelectronics L3G4200D Perspective View

• Note Suspension Springs

o Center enabling rotation

o Auxiliary linear springs

• Note Proof Masses

• Note Anti-Stiction Displacement Motion Constraints


25

• Triaxial Rate Gyroscope Sense Electrode Structure underlying proof mass system

• Note electrodes used for vertical mass displacement

• Note contact electrode structures


26

• Triaxial Rate Gyroscope Measurements:

o Measurement axes

o Consider X axis rotation (vertical and in plane of page for figures above).

§ Now, masses at left and right in the figures above move to left and right in differential motion

§ Coriolis force of V x Ω will yield differential forces acting in the vertical direction (perpendicular to the sensor plane) and sensed by the electrodes shown above at left and right.

o Consider Y axis rotation (horizontal and in plane of page for figures above).

§ Now, upper and lower masses in the figures above move to upwards and downwards in differential motion

§ Coriolis force of V x Ω will yield differential forces acting in the vertical direction (perpendicular to the sensor plane) and sensed by the electrodes shown above at upper and lower locations.

o Now, consider Z axis rotation (vertical and perpendicular to the plane of the page for figures above).

§ Now, masses at left and right in the figures above move to left and right in differential motion

§ Coriolis force of V x Ω will yield differential forces acting in the horizontal in plance direction and sensed by in plane electrodes at left and right and included in the MEMS structure.

§ Note the very much larger area associated with these electrodes as required to establish sufficient capacitance to ensure sensitivity values.


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RATE GYROSCOPE PERFORMANCE: RESPONSIVITY SCALING

• Responsivity does not depend on sensor scale. Mass and R do not appear. Contrast with system consisting of accelerometers where signal vanishes as moment arm and mass go to zero.

• Sensitivity does depend on sensor scale. Thermomechanical noise, below, represents the ultimate limit on mass reduction.

• Also, measurement errors appear

o Mass motion unbalances

o Several error sources - example for non-planar/parallel motion, equal masses, torsional unbalance force. Consider case of simple torsion mounted “tuning fork” gyro.

• Simple calculation allows direct comparison of force-component induced by torsional unbalance and Coriolis force. Both forces lead to torques !

• First, force required to accelerate mass is

Fa = mωd2sinωdt

• But, a component of this force, ΔR/R, acts in the y-direction to creat a torque about Z-axis. Now, this drive force is 900 out of phase with Coriolis force. Thus, the y-axis deflection signal created by this error force may be partially rejected by phase sensitive detection. The ratio of the magnitudes of these two forces is

⎟⎟⎠

⎞⎜⎜⎝

⎛ ΩΔ

=

dA

C

R

RF

F

ω2

• Torsion unbalance signal is an error since it appears as a rotation signal to system.

RrArA

ΔR

Torque

Measurement

RrArA

ΔR

Torque

Measurement


28

• For a system with the parameters above, and earth rotation rate, the signal/error force ratio is one for ΔR/R tolerance of less than 2 x 10-8. The introduction of an accurate phase sensitive detector may relax this requirement to 10-7.

• Clearly, this error source accounts for a substantial bias error - and, therefore, drift.

• Other Error Sources:

o Torsional unbalance misalignment may arise from tolerance of fabrication process and from “out-of-plane” forces of input axis drive mechanism.

o Phase/amplitude imbalance

o Track misalignment - comb drive non-linearity/non-planar forces

o Lateral acceleration error - unequal mass motion excited by lateral acceleration - appears as signal

o Mass imbalance error

o Elastic modulus drift error - torsion suspension properties scale output value and determine bias value. Temperature coefficient of suspension determines system properties.

RrArA

Torque

Measurement

RrArA

Torque

Measurement

RrArA

Torque

Measurement

RrArA

Torque

Measurement


29

9 . MEMS MICROGYROSCOPE OFFSET, OFFSET DRIFT , TEMPERATURE COEFFICIENT AND NOISE

• Data sheet for device is below. Note that responsivity is termed sensitivity and sensitivity is termed rate noise density.

• 8 bit temperature measurement included in L3G4200D module

• Responsivity ranges

o 250, 500, 2000 degrees/sec o Temperature coefficient of responsivity: +/- 2 percent -40 to +85C

• Offset +/- 10 to +/- 75 degrees per second

o Temperature coefficient of offset +/- 0.03 degrees per second temperature coefficient of offset

• Sensitivity o Rate Noise Density o At a measurement bandwidth of 50 Hz: 0.03 degrees/sec-(Hz)1/2 o Typical uncertainty in 1 Hz bandwidth is 0.03 degrees per second rms o Typical uncertainty in 50 Hz bandwidth is 0.2 degrees per second rms


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10 . FREQUENCY -DEPENDENT AND SAMPLING BANDWIDTH -DEPENDENT SENSITIVITY

• The sampling rate and sensitivity relationship is critical

o Engineering design goals will seek to reduce system cost (and reduce performance) until sensitivity requirements are just satisfied with no excess sensitivity

o Thus, sensor systems will generally be found operating at or near their theoretical limits

o It is essential to appreciate the relationship between the parameters of:

§ Sensitivity and resolution

§ Sample rate

§ Noise spectral dependence

• We sample a signal, for example, voltage, v, in time.

o But, we must predict characteristics of sensors in terms of their frequency dependence

o Also, must consider how various spectral regions contribute to noise

• Start with Parseval’s relation the integrated “power” (squared voltage) in a signal over all time is equivalent to an integral over all frequency of the squared modulus of the Fourier transformed voltage.

�

v2(t)

−∞

∞

∫ dt = V ( f )V*( f )

−∞

∞

∫ df

• where the Fourier transform of v(t) is

�

V ( f ) = v(t)ej 2πft

−∞

∞

∫ dt

• Now, is a power spectral density:

o units of V2 per unit inverse frequency (hence density.)

• Consider a band limited signal with signal being zero outside the band of f1 < f < f2

• Can define a root mean square (rms) signal that is conveniently observed by an instrument

2( ) ( )PSD f V f=


31

o Corresponds to a measurement acquired for a bandlimited signal

o Assuming a signal that is continuous in time produces an rms signal that is stationary

• Without proceeding further we can draw an important conclusion about system design

o Consider that PSD is frequency independent

o Consider further in the usual case that the design specification requires establishing a maximum threshold value for rms amplitude

o Then note that this relationship implies that for a reduction of noise by a factor of α requires a decreased in bandwidth of α2

o This also implies an increase in sampling period of α2

• Now, in our systems, we sample signals at a discrete frequency, fS

o But, PSD may be computed in terms will be normalized to a 1 Hz bandwidth

o PSD may be measured at a sample rate other than 1 Hz and referred to a 1 Hz bandwidth (see Chapter 4 of reference text)

• Now, for example accelerometer, compute rms acceleration noise based on fundamental limit

• For this,

MQ

kTPSD O

TNEA

ω4≡

• And,

MQ

kTffdf

MQ

kTdffPSDa O

f

f

O

f

f

RMS

ωω 44)( 12

2

1

2

1

−=== ∫∫

• For the automotive example, the accelerometer that provides a solution is a silicon micromachined devices, for example the Analog Devices ADXL series

2

1

( )

f

rms

f

PSD f dfv = ∫


32

• Here k ∼ 1 N/m, ωo = 2π(2kHz), m ∼ 10-10kg , and Q = 1. Thus, at T = 300K, arms = 0.07 g

• This is significant since even collision detection must occur early in collision cycle when acceleration values are small.

• Also, critical to note:

o This noise signal scales with square root of bandwidth – for frequency independent noise

o In order to achieve a reduction in noise amplitude of factor of 10, bandwidth must be reduced by factor of 100

o This applies as well to integration time in sampling

§ The sample interval implies a bandwidth requirement

• Consider Nyquist rate sampling limitation required to avoid aliasing

§ Consider a decrease in sample rate by a factor of 100 implies, in a Nyquist-limited condition, a factor of 100 times decrease in bandwidth

§ This results in only a 10 times reduction in noise amplitude

§ Note the relation between noise and response time.


33

11 . NOISE SOURCES

• One of the most important sources of noise (and reductions in sensitivity) result from electronic noise sources

o It is very important to note that a fundamental relationship exists between sensor energy requirements and sensitivity

o This must be understood in order to establish a properly optimized (or even feasible) system design

• Electronic noise appears from a wide range of sources. Some are fundamental to measurement processes. These include

o Johnson noise: A fundamental noise source appearing in resistive sensors and semiconductor amplifier elements (piezoresistor, infrared bolometer, Hall magnetometer, field effect transistor, etc.)

o Electron shot noise:

§ A fundamental noise source appearing in semiconductor devices where charge carrier transport through junctions is exploited.

§ Appears in photodetectors where arrival of photon quanta

o Flicker or 1/f noise: A fundamental noise source arising from phenomena including the population and depopulation of individual charge carrier “traps” in semiconductor devices. 1/f noise appears in a broad range of disciplines and appears to be a consequence of ubiquitous switching phenomena.

• Noise impacts system design through both sensitivity and the power required to achieve

sensitivity. • Johnson noise is the voltage noise intrinsic to any resistor, given by

�

VJN

= 4kBTRB

o where B is the bandwidth and kB is Boltzman’s constant .

o To provide an example of its magnitude, for R = 1MΩ, VJN = 128 nanovolt/(Hz)1/2. Johnson noise is important to include in analysis of high-sensitivity piezoresistive transducers, bolometers, and a wide variety of other devices

o This fundamental noise source represents a limit for devices ranging from disk drive read heads to wireless receiver systems.


34

• Electron shot noise is observed for current flow I over (or through) an energy barrier in a pn

junction, Schottky barrier, or tunneling device.

o Due to the discrete nature of electron current flow, and is given by

�

ISN

= 2eIB

o where e is 1.6 x 10-19 C. Again, bandwidth is often neglected so that shot noise is stated in units of A/(Hz)1/2.

o Photon shot noise may limit optical sensors, in particular CCD and CMOS active pixel sensors.

• The largest source of noise at the transducer/amplifier interface is typically transistor amplifier front end noise, since signals at this stage are of lowest amplitude and the effects of noise are greatest.

o Effects of transistor noise in stages following the first amplifier are reduced due to the amplification gain. Thus it is the design of the first amplifier that is critical.

• Bipolar transistor devices show the lowest input noise at low and high frequency for any typical semiconductor device.

o Often, however, the properties of these devices may not be exploited since bipolar devices also present a low input impedance device and so are not compatible with a number of important transducer systems.

• Low frequency performance is limited by 1/f noise. In the bipolar transistor, 1/f noise appears as both a voltage and current signal. The voltage and current noises are

�

Vn = 2efC IBγrb2 1

fα

�

In = 2efC IBγ 1

fα

o where fC is the corner frequency, γ is in the range (1, 2) depending on the device, α ≈ 1, rb is the base resistance and IB is the base current.

o Noise increases below the corner frequency, impacting low frequency sensor stability.


35

o Since both voltage and current noise are present, then an optimization must be performed to select the appropriate value of system input resistance to ensure that these separate contributions result in a minimum noise.

o The input noise increases in limits of both large and small input resistance.

o Typical 1/f flicker noise VN and In values.

§ Assuming a corner frequency of 50 Hz, γ=1, Ib=6.25 x 10-5 A, rB=1 kΩ and α=1,

• At 1 kHz, Vn=1 nV/(Hz)1/2 IN=10-13A/(Hz)1/2

• At 10 Hz, VN=10 nV/(Hz)1/2, In=10-11A/(Hz)1/2

• The MOS field effect transistor (FET) is a high input impedance device, and consequently is compatible with a wide variety of high output resistance transducer systems.

o Characteristics are low input noise at high frequency and 1/f noise.

o Origins of 1/f noise are attributed to charge carrier trapping at interfaces and in the gate insulator. The MOS field effect transistor 1/f noise is

fCWL

KV

ox

n

1

)(=

o for an MOS device of width W, length L, gate capacitance per unit area, Cox , and flicker noise coefficient, K.

• Input-referred, frequency-independent Johnson noise appears also in transistor devices and scales with transistor transconductance and base resistance. Its value is:

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=

m

bBng

rTkV2

14


36

• Johnson noise due to channel resistance also appears in MOS devices.

• In FETs, noise decreases with increasing gm. gm increases with drain current as (ID)1/2. Thus the input stage noise decreases with increasing power dissipation. The noise also decreases with increasing device area.

• Critical result:

o Note that broadband noise scales as fourth root of drain current

o Large increase in drain current and power required to meet sensitivity demand

• Low frequency noise reduction

o Where possible, low frequency noise may be removed through a heterodyning approach

o Prior to being supplied to an input stage, an input signal may be modulated (or “chopped”) with a switching mechanism that preserves signal amplitude properly.

o Then, this high frequency signal may be supplied to a preamp such that its new frequency spectrum lies above the 1/f corner frequency

o After amplification, it may be demodulated.

• The ubiquitous problem of 1/f noise may be eliminated under restricted conditions.

• An important enabling method is signal chopping or heterodyning

o modulates an input low frequency signal and effectively translates this signal to high frequency where amplification may occur in the absence of 1/f noise.

§ Example: non-overlapping clock phases switch the input, ac signal at the clock frequency producing a carrier with amplitude Vi at the output.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

m

Bng

TkV3

24


37

o This technique allows the subsequent use of ac amplifier stages that now operate on this high frequency signal.

o A phase sensitive detector then demodulates the ac signal at the frequency and phase of the modulating clock, rejecting noise at all other frequencies.

o Signal chopping is important in a variety of sensing systems, including optical detectors (which include a light chopper/modulator) and the rate gyroscope (rotation rate provides high-frequency signal) In a number of other sensors the input parameters may also be modulated.

o Direct benefits of signal chopping result from replacing the sensitivity that may have been limited by low frequency 1/f contributions with much lower amplitude broadband noise. This may result in several orders of magnitude improvement in sensitivity.

Phase Sensitive

Detector

Output

Amplifier

ac coupled

gain stage

output signalVi

t

t

_

2

_

1

Phase Sensitive

Detector

Output

Amplifier

ac coupled

gain stage

output signalVi

tt

tt

_

2

_

1


38

12 . SENSOR PERFORMANCE LIMITATIONS EXAMPLE: ACCCELEROMETER

• Now, consider the example of accelerometer and frequency-dependent sensitivity

• The combination of frequency dependent input-referred noise and frequency dependent responsivity lead to a complex sensitivity spectrum that must be considered in design.

• For example, for the accelerometer

�

Responsivity (V/m/s2) =1

ωO

2−ω

2( )2

+ ωOω( )

2Q

2

• Now, consider an input noise spectrum of the form:

vn f( ) = Vn 1+fc

f

⎛⎝⎜

⎞⎠⎟

1/2

V / Hz( )

• where vn is a noise density and Vn = 100 nanovolt/

�

Hz and fc = 100 Hz and with ωo = 2π x 2000 rad/sec and Q = 1. The output signal from this accelerometer will include the product of input signal acceleration and responsivity summed with this voltage noise. These values are typical of the first automotive collision detection sensors and are typical of a device intended for 1 kHz bandwidth operation.

• Responsivity has this form


39

• Sensor system noise has this form

• Sensitivity has this form


40

• Now, let us consider a new system where sensitivity improvement is sought. Resonance frequency may be

reduced from 1000 to 100 Hz. • Can broadband operation be restored?

• Responsivity has this form for 100 Hz resonance frequency


41

• Finally, sensor system sensitivity has this form for 100 Hz resonance frequency

• Note that the improvement in sensitivity at the cost of bandwidth • This now requires a new solution


42

13 . SENSOR SAMPLING AND ENERGY REQUIREMENTS

• Sensor device energy dissipation is divided into transducer demands and the demands associated with

analog front end, digital data conversion, digital signal processing (as required) and feedback control systems (as required).

o Note that many sensors incorporate feedback control and include actuation. Virtually all inertial navigation sensors, for example, include this.

• First, we can review the data conversion process

o The A/D conversion process consists of the steps of anti-alias filtering, sampling, and quantization.

o Some sensors have a narrowband response and may not require further filtering at the desired sampling rates, while in other cases it may be required.

o Next quantization introduces irreversible distortion. o Quantization noise, the difference between the actual signal and the reproduced value,

decreases by 6 dB for each additional bit of quantization. o Each bit typically produces more than a doubling of the power consumption of the device.

• Applications set these requirements

o Example: seismic sensor systems

§ Often, noise and signal sources are separated in frequency

§ Noise present in one spectral region is of much larger amplitude than signal present in other spectral regions

§ Seismic data converters require extreme resolution of 22 – 24 bits at sample rates of up to 1000 Hz

o Example: atmospheric temperature sensor

§ Resolution may only require 10 bits

§ Sample rates may only exceed that of the Nyquist rate for atmospheric variables that may be less than 1 Hz

• Data converter power dissipation

o A figure of merit, for data converters is

o nDissipatioP

HzratesampleresolutionF

))()((=

o A wide range of devices show a value for F of 1010 – 1012

o Example:

• Burr-Brown ADS1210 requires a power of 35mW for conversion of a 200Hz input signal waveform at a resolution of 20 bits.

• F ∼ 6 x 109 (Hz/W)

• LWIM Program Micropower CMOS Sigma-Delta ADC:


43

o 100 Hz sample rate, 9 bit resolution, 30 µW

• F ∼ 1.7 x 109 (Hz/W)

• Sensor Analog Front End Energy Dissipation

o Energy required to meet an established noise level

o Typical micropower CMOS operational amplifiers in current technology display input referred noise of 50 – 100nV/(Hz)1/2 for power supply currents of 1 – 10µA and may operate in weak inversion and are limited to low frequency operation.

o But, noise scales approximately as the fourth root of drain current (in strong inversion mode) operation for a fixed design.

o Reducing this input referred noise to 10nV/(Hz)1/2 may require power supply current greater than 1mA.


44

14 . SENSOR ENERGY REQUIREMENTS

• Energy Requirements for ENS: Sensor Systems

o It is useful to consider sensor types based on transducers available that require low or even no energy for their operation and may be coupled to low power data conversion systems.

o A representative set of sensor and interface systems are listed below.

o Estimated energy demand for data conversion based on current state-of-the-art systems are included.

Sensor Transducer Mechanism

Typical Sampling Rate

Typical Sampling

Resolution

Transducer Bias Power

Analog Front End and Data

Converter Power

Temperature Thermistor 0.01 – 0.1 Hz 10b 100µW 10 - 100µW

Temperature Thermocouple 0.01 – 0.1 Hz 10b 0 100 – 1000µW

Humidity Capacitive (Vaisalla)

0.001 – 0.01 Hz 10b 1mW 10 – 100µW

Vis Light Intensity Photodiode 0.01 – 100Hz 10b 0 10 – 100µW

Infrared Single Pixel Motion

Pyroelectric 0.01 – 100Hz 10b 0 10 – 100µW

Pressure Capacitive 0.001 – 0.01 Hz 10b 1mW 10 – 100µW

Strain Piezoresistive 0.001 – 1 Hz 12 – 24b 100µW 1 – 300mW

Vibration Piezoelectric 0.001 – 1 MHz Hz 10b 0 10µW – 100mW

Vibration Geophone 0.01 – 1000Hz 16 – 24b 0 10µW – 300mW

Microphone Electret 10Hz – 20 kHz 12 – 18b 0 10µW – 300mW

Acceleration Accelerometer DC – 10kHz 10 – 18b 0.1 – 100mW 0.1 – 10mW

Visible Image CMOS APS 1 – 30 fps 10b 10mW 10 – 100mW

Infrared Thermal Imager

Bolometer Array 1 – 10 fps 10b 1W 500mW

Visible Imager High resolution CCD

1 – 30 fps 24b 1W 1W

.


45

15 . SEISMIC SENSOR CASE STUDY

• Current Technology: Reftek Seismic Sensor Interface

o 3 three channel instrument operating with three geophone sensors

o Geophone velocity sensors

§ Require no bias energy

§ May be implemented with low resonant frequency structures

§ Sensitivity ~ 10-7 g/(Hz)1/2

§ Structure

1. suspended proof mass

2. proof mass and magnet combined

3. coil surrounds magnet/mass

• Operation

• Reftek System Design Requirements

o Sensor sensitivity requirement must match inherent noise of geophone

§ Limited by resistance of geophone element ~ 100Ω - 1000Ω

§ Geophone noise (in absence of motion) ~ 1.3 – 40 nV/(Hz)1/2

coil

proof

mass

magnet

flexure

coilflexure

proof

mass

magnet

coil

proof

mass

magnet

flexure

coilflexure

proof

mass

magnet


46

o Preamplifer input referred noise must not exceed this sensor noise (to achieve optimal sensitivity)

§ Note drain current to input referred noise relationship

§ Amplifiers that meet this requirement show 100mW power dissipation

§ 300mW total power

o Time synchronization

§ Recall discussion of sampling time control

§ Seismic application requires 1 micro-s/week drift

§ Uses temperature compensated crystal oscillator TCXO - 50 mW

o Processor

§ ARM 9

§ Power dissipation: 100 mW

§ Processor chosen to match peripheral requirements

o ADC

§ 24b resolution with 200 samples/sec

§ Submicrosecond resolution on sample timing – low jitter sampling

§ Power dissipation: 50mW/channel

o Architecture

§ Single RAM memory bank

§ ASIC (FPGA) memory access abritrator

§ ADC system writes via DMA to RAM

§ Processor reads from RAM and writes to storage

o New Design requirements

§ Rapidly deployed wireless networked seismometer

§ Will merge LEAP platform with Reftek platform

§ Energy and performance advances

§ Negligible cost impact


47

16 . POLYMER RESISTIVE PRESSURE SENSORS

• Conducting polymer

o Composite material

§ Carbon nanometer scale particles (carbon black)

1. High electrical conductance

2. High elastic modulus

§ Insulating matrix

1. Low elastic modulus

o Exploits principle of percolation

§ Resistivity of medium reduces with increasing volume fraction of conducting particles

o Application of pressure reduces resistance of resistor system composed of pressure sensitive conducting polymer

17 . OPTICAL BIOMEDICAL SENSOR SYSTEMS

• Optical biomedical sensors are available or under development for:

o Blood oxygen saturation

o Blood glucose concentration

o Nutrition biomarkers

• Blood oxygen saturation sensors provide a non-invasive, low cost, accurate measurement system.

• Principles:

o Hemoglobin – globular protein in blood providing oxygen-transport dependent on an oxygen ion – iron bond

• Oxy-hemoglobin: Oxygenated hemoglobin

• Deoxy-hemoglobin: Reduced hemoglobin


48

• Myoglobin – oxygen storage protein incorporated in tissue

( Combined data set by Scott Prahl, Oregon Medical Laser Center )

• Optical absorption spectroscopy shows that absorption of oxy-hemoglobin and deoxy-hemoglobin is equal near 800 nm and at longer wavelength

• Optical transmittance, T, (for large transmittance and small absorbance) follows Beer’s Law:

T = 10−αcd

• where α is the absorption coefficient (per mole per cm3), c is the concentration in moles per cm3 and d is the optical path length in the medium

• This enables design of a detector for blood oxygen

o First, this can be designed for measurement of transmission of light through tissue (for example a finger tip).

o Now light propagates through tissue and encounters tissue containing no blood, or venous blood (deoxygenated hemoglobin blood returning in veins to the heart), and arterial blood (oxygenated hemoglobin blood arriving from the heart).

o Arterial blood arrives with a time varying pressure that follows cardiac pump activity. Arterial blood volume fluctuates in synchronization with pulse activity.

100

1000

10000

100000

1000000

250 450 650 850

Wavelength (nm)

Ab

so

rb

tio

n C

oeff

icie

nt

per

Mo

le (

1/

cm

)HbO2

Hb


49

• Pulse oximeter design exploits characteristics of light propagation through tissue

o Cost constraints limit choice of light sources

o Use semiconductor LED devices:

• (near infrared devices) at 840 nm for detection of both oxy- and deoxy-hemoglobin

• Visible (red) LED at 660 nm for detection of oxy-hemoglobin

o Two LED sources used (operating modulated in time) and a single detector.

o Resolve time dependent signal and pulse rate

o Resolve amplitude of absorption to compute (via model relationship) blood oxygen saturation as a fraction of complete saturation.

ee180d systems design sensor systems 1

Documents

sensor sampling

accelerometer sensor

sensor technology

accelerometer sensor

sensor system overview

rate gyroscope performance

sensor energy requirements

triaxial rate gyroscope