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Lecture 9 Sensors, A/D, sampling noise and jitter

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voltage divider Vsignal = ( 5V) RR/(R RR) Choose R=RR at median of ... B. A leads B. Phase lag between A and B is 90 degrees (Quadrature Encoder) Jizhong Xiao ... – PowerPoint PPT presentation

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Title: Lecture 9 Sensors, A/D, sampling noise and jitter


1
Lecture 9Sensors, A/D, sampling noise and jitter
  • Forrest Brewer

2
Light Sensors - Photoresistor
  • voltage divider Vsignal (5V) RR/(R RR)
  • Choose RRR at median of intended measured range
  • Cadmium Sulfide (CdS)
  • Cheap, relatively slow (low current)
  • tRC Cl(RRR)
  • Typically R50-200kW C20pF so tRC20-80uS gt
    10-50kHz

3
Light Sensors - Phototransistor
  • Much higher sensitivity
  • Relatively slow response (1-5uS due to collector
    capacitance)

4
Light Sensors - Pyroelectric Sensors
  • lithium tantalate crystal is heated by thermal
    radiation
  • tuned to 8-10 ?m radiation maximize response to
    human IR signature
  • motion detecting burglar alarm
  • E.g. Eltec 442-3 sensor - two elements, Fresnel
    optics, output proportional to the difference
    between the charge on the left crystal and the
    charge on the right crystal.

5
Other Common Sensors
  • Force
  • strain gauges - foil, conductive ink
  • conductive rubber
  • rheostatic fluids
  • Piezorestive (needs bridge)
  • piezoelectric films
  • capacitive force
  • Charge source
  • Sound
  • Microphones
  • Both current and charge versions
  • Sonar
  • Usually Piezoelectric
  • Position
  • microswitches
  • shaft encoders
  • gyros
  • Acceleration
  • MEMS
  • Pendulum
  • Monitoring
  • Battery-level
  • voltage
  • Motor current
  • Stall/velocity
  • Temperature
  • Voltage/Current Source
  • Field
  • Antenna
  • Magnetic
  • Hall effect
  • Flux Gate
  • Location
  • Permittivity
  • Dielectric

6
Incidence -- photoreflectors
7
Rotational Position Sensors
  • Optical Encoders
  • Relative position
  • Absolute position
  • Other Sensors
  • Resolver
  • Potentiometer

Jizhong Xiao
8
Optical Encoders
mask/diffuser
  • Relative position

light sensor
decode circuitry
light emitter
grating
Jizhong Xiao
9
Optical Encoders
  • Relative position

- direction
light sensor
- resolution
decode circuitry
light emitter
Phase lag between A and B is 90 degrees
(Quadrature Encoder)
Ronchi grating
A
B
A leads B
Jizhong Xiao
10
Optical Encoders
  • Detecting absolute position
  • Typically 4k-8k/2p
  • Higher Resolution Available Laser/Hologram
    (0.1-0.3 resolution)

Jizhong Xiao
11
Gray Code
0000 0001 0011 0010 0110 0111 0101 0100 1100 .. 10
01
  • Almost universally used encoding
  • One transition per adjacent number
  • Eliminates alignment issue of multiple bits
  • Simplified Logic
  • Eliminates position jitter issues
  • Recursive Generalization of 2-bit quadrature code
  • Each 2n-1 segment in reverse order as next bit is
    added
  • Preserves unambiguous absolute position and
    direction

Jizhong Xiao
12
Other Motor Sensors
  • Resolver
  • Selsyn pairs (1930-1960)
  • High speed
  • Potentiometer
  • High resolution
  • Monotone but poor linearity
  • Noise!
  • Deadzone!

Jizhong Xiao
13
Draper Tuning Fork Gyro
  • The rotation of tines causes the Coriolis Force
  • Forces detected through either electrostatic,
    electromagnetic or piezoelectric.
  • Displacements are measured in the Comb drive

14
Improvement in MEMS Gyros
  • Improvement of drift
  • Little drift improvement in last decade
  • Controls/Fabrication issue
  • Improvement of resolution

15
Piezoelectric Gyroscopes
  • Basic Principles
  • Piezoelectric plate with vibrating thickness
  • Coriolis effect causes a voltage form the
    material
  • Very simple design and geometry

16
Piezoelectric Gyroscope
  • Advantages
  • Lower input voltage than vibrating mass
  • Measures rotation in two directions with a single
    device
  • More Robust
  • Disadvantages
  • (much) Less sensitive
  • Output is large when O 0
  • Drift compensation

17
Absolute Angle Measurement
  • Bias errors cause a drift while integrating
  • Angle is measured with respect to the casing
  • The mass is rotated with an initial ?
  • When the gyroscopes rotates the mass continues to
    rotate in the same direction
  • Angular rate is measured by adding a driving
    frequency ?d

18
Design consideration
  • Damping needs to be compensated
  • Irregularities in manufacturing
  • Angular rate measurement

For angular rate measurement
Compensation force
19
Measurement Accuracy vs. Precision
  • Expectation of deviation of a given measurement
    from a known standard
  • Often written as a percentage of the possible
    values for an instrument
  • Precision is the expectation of deviation of a
    set of measurements
  • standard deviation in the case of normally
    distributed measurements
  • Few instruments have normally distributed errors

20
Deviations
  • Systematic errors
  • Portion of errors that is constant over data
    gathering experiment
  • Beware timescales and conditions of experiment
    if one can identify a measurable input parameter
    which correlates to an error the error is
    systematic
  • Calibration is the process of reducing systematic
    errors
  • Both means and medians provide estimates of the
    systematic portion of a set of measurements

21
Random Errors
  • The portion of deviations of a set of
    measurements which cannot be reduced by knowledge
    of measurement parameters
  • E.g. the temperature of an experiment might
    correlate to the variance, but the measurement
    deviations cannot be reduced unless it is known
    that temperature noise was the sole source of
    error
  • Error analysis is based on estimating the
    magnitude of all noise sources in a system on a
    given measurement
  • Stability is the relative freedom from errors
    that can be reduced by calibration not freedom
    from random errors

22
Model based Calibration
  • Given a set of accurate references and a model of
    the measurement error process
  • Estimate a correction to the measurement which
    minimizes the modeled systematic error
  • E.g. given two references and measurements, the
    linear model

23
Noise Reduction Filtering
  • Noise is specified as a spectral density
    (V/Hz1/2) or W/Hz
  • RMS noise is proportional to the bandwidth of the
    signal
  • Noise density is the square of the transfer
    function
  • Net (RMS) noise after filtering is

24
Filter Noise Example
  • RC filtering of a noisy signal
  • Assume uniform input noise, 1st order filter
  • The resulting output noise density is
  • We can invert this relation to get the equivalent
    input noise

25
Averaging (filter analysis)
  • Simple processing to reduce noise running
    average of data samples
  • The frequency transfer function for an N-pt
    average is
  • To find the RMS voltage noise, use the previous
    technique
  • So input noise is reduced by 1/N1/2

26
Normal Gaussian Statistics
  • Mean
  • Standard Deviation
  • Note that this is not an estimate for a total
    sample set (issue if Nltlt100), use 1/(N-1)
  • For large set of data with independent noise
    sources the distribution is
  • Probability

27
Issues with Normal statistics
  • Assumptions
  • Noise sources are all uncorrelated
  • All Noise sources are accounted for
  • Enough time has elapsed to cover events
  • In many practical cases, data has outliers
    where non-normal assumptions prevail
  • Cannot Claim small probability of error unless
    sample set contains all possible failure modes
  • Mean may be poor estimator given sporadic noise
  • Median (middle value in sorted order of data
    samples) often is better behaved
  • Not used often since analysis of expectations are
    difficult

28
Characteristic of ADC and DAC
  • DAC
  • Monotonic and nonmonotonic
  • Offset , gain error , DNL and INL
  • Glitch
  • Sampling-time uncertainty
  • ADC
  • missing code
  • Offset , gain error , DNL and INL
  • Quantization Noise
  • Sampling-time uncertainty

29
Monotonic and missing code
If DNL lt - 1 LSB gt missing code. (A/D)
30
Offset and Gain Error
D/A
A/D
31
D/A nonlinearity (D/A)
Differential nonlinearity (DNL)
Maximum deviation of the analog output step from
the ideal value of 1 LSB .
Integral nonlinearity (INL) Maximum deviation of
the analog output from the ideal value.
32
D/A nonlinearity (A/D)
  • Differential nonlinearity (DNL) Maximum
    deviation in step width (width between
    transitions) from the ideal value of 1 LSB
  • Integral nonlinearity (INL) Maximum deviation of
    the step midpoints from the ideal step midpoints.
    Or the maximum deviation of the transition points
    from ideal.

33
Glitch (D/A)
  • I1 represents the MSB current
  • I2 represents the N-1 LSB current
  • ex01111 to 10000

34
Sampling Theorem
  • Perfect Reconstruction of a continuous-time
    signal with Band limit f requires samples no
    longer than 1/2f
  • Band limit is not Bandwidth but limit of
    maximum frequency
  • Any signal beyond f aliases the samples

35
Aliasing (Sinusoids)
36
Aliased Reconstruction
  • Reconstruction assumes values on principle branch
    usually lower frequency
  • Nyquist Theorem assumes infinite history is
    available
  • Aliasing issues are worse for finite length
    samples
  • Dont crowd Nyquist limits!

37
Alaising
  • For Sinusoid signals (natural band limit)
  • For Cos(wn), w2pkw0
  • Samples for all k are the same!
  • Unambiguous if 0ltwltp
  • Thus One-half cycle per sample
  • So if sampling at T, frequencies of fe1/2T will
    map to frequency e

38
Quantization Effects
  • Samples are digitized into finite digital
    resolution
  • Shows up as uniform random noise
  • Zero bias (for ideal A/D)

39
Quantization Error
lsb/2
x
-lsb/2
  • Deviations produced by digitization of analog
    measurements
  • For white, random signal with uniform
    quantization of xlsb

40
Quantization Noise (A/D)
41
Quantization Noise
  • Uniform Random Value
  • Bounded range VLSB/2, VLSB/2
  • Zero Mean

42
Sampling Jitter (Timing Error)
  • Practical Sampling is performed at uncertain time
  • Sampling interval noise measured as value error
  • Sampling timing noise also measured as value
    error

43
Sampling-Time Uncertainty
  • (Aperture Jitter)
  • Assume a full-scale sinusoidal input,
  • want
  • then

44
Jitter Noise Analysis
  • Assume that samples are skewed by random amount
    tj
  • Expanding v(t) into a Taylor Series
  • Assuming tj to be small

45
Sampling Jitter Bounds
  • Error signal is proportional to the derivative
  • Bounding the bandwidth bounds the derivative
  • For tRMS, the RMS noise is
  • If we limit vRMS to LSB we can bound the jitter
  • So for a 1MHz bandwidth, and 12 bit A/D we need
    less than 100pS of RMS jitter

46
DAC Timing Jitter
  • DAC output is convolution of unit steps
  • Jitter RMS error depends on both timing error and
    sample period

Dv
tj
47
DAC Timing Jitter
  • Error is
  • Energy error
  • RMS jitter error
  • Relating to continuous time

48
DAC Jitter Bounds
  • We can use the same band limit argument as for
    sampling to find the jitter bound for a D-bit
    DAC
  • So a 10MHz, 5-bit DAC can have at most 85pS of
    jitter.

49
Decoder-Based D/A converters
  • Inherently monotonic.
  • DNL depend on local matching of neighboring R's.
  • INL depends on global matching of the R-string.

50
Decoder-Based D/A converters
  • 4-bit folded R-string D/A converter

51
Decoder-Based D/A converters
  • Multiple R-string 6-bit D/A converter
  • interpolating

52
Decoder-Based D/A converters
  • R-string DACs with binary-tree decoding.
  • Speed is limited by the delay through the
    resistor string as well as the delay through the
    switch network.

53
Binary-Scaled D/A Converters
  • Monotonicity is not guaranteed.
  • Potentially large glitches due to timing skews.

Current-mode converter
54
Binary-Scaled D/A Converters
Binary-array charge-redistribution D/A converter
  • 4 bit R-2R based D/A converter
  • No wide-range scaling of resistors.

55
Thermometer-Code Converter
56
Flash (Parallel) Converters
  • High speed. Requires only one comparison cycle
    per conversion.
  • Large size and power dissipation for large N.

57
Feedback in Sensing/Conversion
  • High Resolution and Linearity Converters
  • Very expensive to build open-loop (precision
    components)
  • Aging, Drift, Temperature Compensation
  • Closed-Loop Converters
  • Much higher possible resolution
  • Greatly improved linearity
  • Can use inexpensive components by substituting
    amplifier gain for component precision
  • But
  • Higher Measurement Latency
  • Decreased Bandwidth
  • Eg. Successive Approx, Sigma-Delta

58
Nyquist-Rate A/D converters
59
Integrating converters
  • Low conversion rate.

60
Successive-Approximation Converters
  • Binary search

61
Successive-Approximation Converters
  • DAC-based successive-approximation converter.
  • Requires a high-speed DAC with precision on the
    order of the converter itself.
  • Excellent trade-off between accuracy and speed.
    Most widely used architecture for monolithic A/D.

62
Sigma Delta A/D Converter
en
Decimation Filter
fs
fs
2 fo
Sampler
Modulator
x(t)
xn
yn
16 bits
Bandlimited to fo
Digital
Analog
Over Sampling Ratio 2fo is Nyquist
frequency Transfer function for an Lth order
modulator given by
63
Modulator Characteristics
  • Highpass character for noise transfer function
  • In-band noise power is given by
  • no falls by 3(2L1) for doubling of Over Sampling
    Ratio
  • L0.5 bits of resolution for doubling of Over
    Sampling Ratio
  • no essentially is uncorrelated for
  • Dithering is used to decorrelate quantization
    noise
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