– 1 – Data Converters Data Converter Basics Professor Y. Chiu - PowerPoint Presentation

Slide1

– 1 –

Data Converters Data Converter Basics Professor Y. ChiuEECT 7327 Fall 2014

Data Converter BasicsSlide2

A/D and D/A Conversion–

2 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

A/D Conversion

D/A ConversionSlide3

Quantization–

3 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Quantization = division + normalization + truncation

Full-scale range (V

FS

) is determined by V

refSlide4

Quantization Error–

4 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

“Random” quantization error is usually regarded as noise

N = 3Slide5

Quantization Noise–

5 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Assumptions

:

N is large

0

≤

V

in

≤

V

FS

and V

in

>>

Δ

V

in

is active

ε

is

Uniformly distributed

Spectrum of

ε

is whiteRef: W. R. Bennett, “Spectra of quantized signals,” Bell Syst. Tech. J., vol. 27, pp. 446-472, July 1948.Slide6

Signal-to-Quantization Noise Ratio (SQNR)

– 6 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Assume V

in

is sinusoidal with

V

p

-p

=

V

FS

,

N

(bits)

SQNR

(dB)

8

49.9

10

62.0

12

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.)Slide7

FFT Spectrum of Quantized Signal

– 7 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

N = 10 bits

8192 samples, only

f

= [0, fs

/2] shown

Normalized to V

in

f

s

= 8192,

fin = 779fin and fs must be

incommensurate

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.Slide8

Commensurate fs and

fin–

8

–

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

f

s

= 8192

f

in

= 256

f

s

= 8192

f

in

= 2048

Periodic sampling points result in periodic quantization errors

Periodic quantization errors result in harmonic distortionSlide9

Spectrum Leakage–

9 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

f

s

= 8192

f

in

= 779.3

f

s

= 8192

f

in

= 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

windowSlide10

FFT Spectrum with Distortion

– 10 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

High-order harmonics are aliased back, visible in

[0,

f

s

/2] bandE.g., HD3 @ 779x3+1=2338, HD9 @ 8192-9x779+1=1182

HD3

HD9Slide11

Dynamic Performance–

11 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Peak SNDR limited by large-signal distortion of the converter

Dynamic range implies the “theoretical” SNR of the converterSlide12

Dynamic Performance Metrics

– 12 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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 convertersSlide13

Evaluating Dynamic Performance

– 13 –

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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

HD3

HD9Slide14

Static Performance Metrics

– 14 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Offset (OS)

Gain error (GE)

Monotonicity

Linearity (unique to

converters)

Differential nonlinearity (DNL

)

Integral nonlinearity (INL)Slide15

– 15 –

Data Converters Data Converter Basics Professor Y. ChiuEECT 7327 Fall 2014

Static Performance

of DACSlide16

DAC Transfer Characteristic

– 16 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Note

: V

out

(bi = 1, for all i) = VFS - Δ = VFS

(1-2-N) ≠ VFS

N = # of bits

V

FS

= Full-scale input

Δ

= V

FS

/2

N

= 1LSB

b

i

= 0 or 1

MultiplicationSlide17

Ideal DAC Transfer Curve–

17 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014Slide18

Offset–

18 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

V

osSlide19

Gain Error–

19 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014Slide20

Monotonicity–

20 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014Slide21

Differential and Integral Nonlinearities

– 21 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

DNL = deviation of an output step from 1 LSB (=

Δ

= V

FS

/2N)INL = deviation of the output from the ideal transfer curve

DNL < -1 ?Slide22

DNL and INL–

22 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

INL = cumulative sum of DNLSlide23

DNL and INL–

23 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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).

Smooth

NoisySlide24

Measure DNL and INL (Method I)

– 24 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Endpoints of the transfer characteristic are always at 0 and V

FS

-

Δ

Endpoint

stretchSlide25

Measure DNL and INL (Method II)

– 25 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Least-square

fit and stretch

(“detrend”)

Endpoints of the transfer characteristic may not be at 0 and V

FS

-

ΔSlide26

Measure DNL and INL–

26 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Method I (endpoint stretch)

Σ

(

INL) ≠ 0

Method II (LS fit & stretch)Σ(INL) = 0Slide27

– 27 –

Data Converters Data Converter Basics Professor Y. ChiuEECT 7327 Fall 2014

Static Performance

of ADCSlide28

Ideal ADC Transfer Characteristic

– 28 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Note the systematic offset! (floor, ceiling, and round)Slide29

DNL and Missing Code–

29 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

DNL = deviation of an input step width from 1 LSB (

= V

FS

/2

N

=

Δ

)

DNL = ?

Can DNL < -1?Slide30

DNL and Nonmonotonicity

– 30 –

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

DNL = deviation of an input step width from 1 LSB (

= V

FS

/2

N

=

Δ

)

DNL = ?

How can we even measure this?Slide31

INL–

31 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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

(method I and II …)

Any code

Missing?

Nonmonotonic?Slide32

10-bit ADC Example–

32 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

1024 codes

No missing code!

Plotted against the digital code, not V

in

Code density test (CDT)

DNL must always be greater or equal to -1 LSB!Slide33

Code Density Test–

33 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Ball casting problem: # of balls collected by each bin (n

i

) is proportional to the bin size (converter step size)Slide34

CDT and Nonmonotonicity

– 34 –

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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

CDT can be misleading in determining the static nonlinearitySlide35

– 35 –

Data Converters Data Converter Basics Professor Y. ChiuEECT 7327 Fall 2014

Nyquist

-Rate ADCSlide36

Nyquist-Rate ADC

– 36 –

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Digitizes input signal up to Nyquist frequency (

f

N

=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 digitizationSlide37

Nyquist-Rate ADC (N-Bit, Binary)

– 37 –

Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

Word-at-a-time (1 step)

†

←

fastFlashLevel-at-a-time (2

N

steps)

←

slowest

Integrating (Serial)

Bit-at-a-time (N steps)

← slowSuccessive approximationAlgorithmic (Cyclic)

Partial word-at-a-time (1 < M

≤

N steps)

←

medium

Subranging

Pipeline

Others (1

≤

M

≤

N step)Folding ← relatively fastInterleaving (of flash, pipeline, or SA) ←

fastest

† the number in the parentheses is the “latency” of conversion, not “throughput”Slide38

Accuracy-Speed Tradeoff–

38 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014Slide39

Building Blocks for Data Converters

– 39 –Data Converters Data Converter Basics Professor Y. Chiu

EECT 7327

Fall 2014

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

Switched-Capacitor Amplifiers, Integrators, and Filters

Operational Amplifier

Comparators (Preamplifier and Latch)

Voltage and Current DAC’s

Current Sources

Voltage/Current/

Bandgap

References