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    1

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Data Converter Basics

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    A/D and D/A Conversion

    2

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    S/H

    Analog

    in

    Digital

    out

    Quantization

    DSP

    AAF

    S/H

    AnalogoutDigitalin

    D/A

    DSP

    Smoothing

    filter

    A/D Conversion

    D/A Conversion

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    Quantization

    3

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    N inout

    FS

    VDivision : D = 2

    V

    Quantization = division + normalization + truncation

    Full-scale range (VFS) is determined by Vref

    A/Dbn

    Digital outputAnalog input

    b1...

    Vref

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    Quantization Error

    4

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    FSout in out inN

    V = D - V =D - V

    2

    FS

    N

    V = =LSB

    2

    in FSV 0, V

    - 2 2

    Dout

    0

    Vin

    2 3

    1

    3

    5

    0

    2

    4

    6

    7

    VFS

    2

    --2-3

    VFS

    2

    Random quantization error

    is usually regarded as noise

    Vin0

    -/2

    /2

    2 30--2-3

    N = 3

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    Quantization Noise

    5

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vin

    2 3

    0

    4 5 6 7-/2

    /2

    VFS

    /2 2

    2 2

    -/2

    1 = d =

    12

    P

    0-/2 /2

    1/

    Assumptions:

    N is large

    0 Vin VFSand Vin>>

    Vinis active

    is Uniformly distributed

    Spectrum of is white

    Ref: W. R. Bennett, Spectra of quantized signals, Bell Syst. Tech. J., vol. 27, pp. 446-472, July 1948.

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    Signal-to-Quantization Noise Ratio (SQNR)

    6

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    2N2

    2NFS

    22

    2 / 8V / 8SQNR = = =1.5 2 ,

    12

    Assume Vinis sinusoidal with Vp-p= VFS,

    SQNR = 6.02 N+1.76 dB

    N

    (bits)

    SQNR

    (dB)

    8 49.9

    10 62.012 74.0

    14 86.0

    SQNR depicts the theoretical performance of an ideal ADC In reality, ADC performance is limited by many other factors:

    Electronic noise (thermal, 1/f, coupling/substrate, etc.)

    Distortion (measured by THD, SFDR, IM3, etc.)

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    FFT Spectrum of Quantized Signal

    7

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    N = 10 bits

    8192 samples, only

    f= [0, fs/2] shown

    Normalized to Vin

    fs= 8192, fin= 779

    finand fsmust be

    incommensurate

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    dB

    SQNR-1.76 dBENOB=6.02 dB

    SQNR = 61.93 dB

    ENOB = 9.995 bits

    Ref: W. R. Bennett, Spectra of quantized signals, Bell Syst. Tech. J., vol. 27, pp. 446-472, July 1948.

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    Commensuratefsand fin

    8

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    d

    B

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    d

    B

    fs= 8192

    fin= 256

    fs= 8192

    fin= 2048

    Periodic sampling points result in periodic quantization errors

    Periodic quantization errors result in harmonic distortion

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    Spectrum Leakage

    9

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    d

    B

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    d

    B

    fs= 8192

    fin= 779.3

    fs= 8192

    fin= 779.3

    TD samples must include integer number of cycles of input signal

    Windowing can be applied to eliminate spectrum leakage

    Trade-off b/t main-lobe width and sideband rejection for different windows

    w/

    Blackman

    window

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    FFT Spectrum with Distortion

    10

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    dB

    High-order harmonics are aliased back, visible in [0, fs/2] band

    E.g., HD3 @ 779x3+1=2338, HD9 @ 8192-9x779+1=1182

    HD3HD9

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    Dynamic Performance

    11

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    SNDR

    [dB]

    Vin[dB]0 VFS

    Overload

    Peak SNDR limited by large-signal distortion of the converter

    Dynamic range implies the theoretical SNR of the converter

    2

    in10 2 2

    N

    in

    SNR

    V / 2=10LOG

    /12+

    V dB

    Peak

    SNDR

    Dynamic

    range

    Circuit

    noise

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    Dynamic Performance Metrics

    12

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Signal-to-noise ratio (SNR)

    Total harmonic distortion (THD)

    Signal-to-noise and distortion ratio (SNDR or SINAD)

    Spurious-free dynamic range (SFDR)

    Two-tone intermodulation product (IM3)

    Aperture uncertainty (related to the frontend S/H and clock)

    Dynamic range (DR)misleading (avoid it if possible!) Idle channel noise or pattern noise in oversampled converters

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    Evaluating Dynamic Performance

    13

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0 500 1000 1500 2000 2500 3000 3500 4000-120

    -100

    -80

    -60

    -40

    -20

    0

    PSD

    Frequency

    dB

    Signal-to-noise

    plus distortion ratio

    (SNDR)

    Total harmonic

    distortion (THD)

    Spurious-free

    dynamic range

    (SFDR)

    SNDR = 59.16 dB

    THD = 63.09 dB

    SFDR = 64.02 dB

    ENOB = 9.535 bits

    HD3HD9

    SNDR -1.76 dBENOB =

    6.02 dB

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    Static Performance Metrics

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Offset (OS)

    Gain error (GE)

    Monotonicity

    Linearity

    Differential nonlinearity (DNL)

    Integral nonlinearity (INL)

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Static Performance

    of DAC

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    DAC Transfer Characteristic

    16

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Note: Vout(bi= 1, for all i) = VFS-= VFS(1-2-N) VFS

    N N

    N-iiout FS ii

    i=1 i=1

    bV = V = b 2

    2

    D/Abn

    Digital input

    Vout

    Analog output

    b1...

    Vref

    N = # of bits

    VFS= Full-scale input

    = VFS/2N= 1LSB

    bi= 0 or 1

    Multiplication

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    Ideal DAC Transfer Curve

    17

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000Din

    001 011 101010 100 110 111

    VFS-

    VFS2

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    Offset

    18

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Vos

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    Gain Error

    19

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

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    Monotonicity

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

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    Differential and Integral Nonlinearities

    21

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    DNL = deviation of an output step from 1 LSB (== VFS/2N)

    INL = deviation of the output from the ideal transfer curve

    DNL < -1 ?

    Vout

    000

    Din

    001 011 101010 100 110 111

    VFS2

    INL

    VFS-

    th

    i

    i Step Size- DNL =

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    DNL and INL

    22

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000

    Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    i

    i j

    j=0

    INL = DNL

    INL = cumulative sum of DNL

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    DNL and INL

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    DNL measures the uniformity of quantization steps, or incremental (local)

    nonlinearity; small input signals are sensitive to DNL.

    INL measures the overall, or cumulative (global) nonlinearity; large input

    signals are often sensitive to both INL (HD) and DNL (QE).

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Smooth Noisy

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    Measure DNL and INL (Method I)

    24

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000

    Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Endpoints of the transfer characteristic are always at 0 and VFS-

    Endpointstretch

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    Measure DNL and INL (Method II)

    25

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Vout

    000

    Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Least-squarefit and stretch

    (detrend)

    Endpoints of the transfer characteristic may not be at 0 and VFS-

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    Measure DNL and INL

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Method I (endpoint stretch)

    (INL) 0

    Method II (LS fit & stretch)

    (INL) = 0

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

    Vout

    000Din

    001 011 101010 100 110 111

    VFS2

    VFS-

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Static Performance

    of ADC

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    Ideal ADC Transfer Characteristic

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Dout

    000 Vin

    001

    011

    101

    010

    100

    110

    111

    VFSVFS/20

    Note the systematic offset! (floor, ceiling, and round)

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    DNL and Missing Code

    29

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Dout

    000 Vin

    001

    011

    101

    010

    100

    110

    111

    VFSVFS/20

    DNL = deviation of an input step width from 1 LSB (= VFS/2N=)

    DNL = ?

    Can DNL < -1?

    th

    i

    i Step Size- DNL =

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    DNL and Nonmonotonicity

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    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Dout

    000 Vin

    001

    011

    101

    010

    100

    110

    111

    VFSVFS/20

    DNL = deviation of an input step width from 1 LSB (= VFS/2N=)

    DNL = ?

    How can we even

    measure this?

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    INL

    31

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Dout

    000 Vin

    001

    011

    101

    010

    100

    110

    111

    VFSVFS/20

    INL = deviation of the step midpoint from the ideal step midpoint

    (method I and II )

    Any code

    Missing?

    Nonmonotonic?

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    10-bit ADC Example

    32

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0 200 400 600 800 1000-2

    -1

    0

    1

    2DNL

    LSB

    0 200 400 600 800 1000-2

    -1

    0

    1

    2INL

    Code

    LSB

    1024 codes

    No missing code!

    Plotted againstthe digital code,

    not Vin

    Code density test

    (CDT)

    DNL must always be greater or equal to -1 LSB!

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    Code Density Test

    33

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Count

    000Vin

    001 011 101010 100 110 111

    VFS0

    Uniformly distributed 0 Vin VFS

    n

    n

    n

    n

    n

    n

    n

    n

    Ball casting problem: # of balls collected by each bin (ni) is proportional to

    the bin size (converter step size)

    th

    i ii

    i

    n - ni Step Size-DNL =

    n

    Count

    000Vin

    001 011 101010 100 110 111

    VFS0

    Uniformly distributed 0 Vin VFS

    >

    ni

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    CDT and Nonmonotonicity

    34

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Two transition steps for one code?! How to plot INL/DNL?

    CDT can be misleading in determining the static nonlinearity

    Dout

    000 Vin

    001

    011

    101

    010

    100

    110

    111

    VFSVFS/20

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    35

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Nyquist-Rate ADC

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    Nyquist-Rate ADC

    36

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Digitizes input signal up to Nyquist frequency (fN=fs/2)

    Minimum sample rate (fs) for a given input bandwidth

    Each sample is digitized to the maximum resolution of converter

    Often referred to as the black box version of digitization

    A/Dbn

    Digital outputAnalog inputb1

    ...

    Vref

    fs

    D C D C B i P f Y Chi

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    Nyquist-Rate ADC (N-Bit, Binary)

    37

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Word-at-a-time (1 step) fast

    Flash

    Level-at-a-time (2Nsteps) slowest

    Integrating (Serial)

    Bit-at-a-time (N steps) slow

    Successive approximation

    Algorithmic (Cyclic)

    Partial word-at-a-time (1 < M N steps) medium

    Subranging

    Pipeline

    Others (1 M N step)

    Folding relatively fast

    Interleaving (of flash, pipeline, or SA) fastest

    the number in the parentheses is the latency of conversion, not throughput

    D t C t D t C t B i P f Y Chi

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    Accuracy-Speed Tradeoff

    38

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    0

    Resolution

    [Bits]

    5

    10

    15

    20

    1k 10k 100k 1M 10M 100M 1G 10G

    Sample Rate [Hz]

    Nyquist

    Oversampling

    Integrating Oversampling

    Successive Approximation

    AlgorithmicSubranging

    Pipeline

    Folding & Interpolating

    FlashInterleaving

    1 level/Tclk1 word/OSR*Tclk

    1 bit/Tclk

    Partial word/Tclk

    1 word/Tclk

    100G

    D t C t D t C t B i P f Y Chi

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    Building Blocks for Data Converters

    39

    Data Converters Data Converter Basics Professor Y. Chiu

    EECT 7327 Fall 2012

    Sample-and-Hold (Track-and-Hold) Amplifier

    Switched-Capacitor Amplifiers, Integrators, and Filters

    Operational Amplifier

    Comparators (Preamplifier and Latch)

    Voltage and Current DACs

    Current Sources

    Voltage/Current/Bandgap References