Introduction to ADC Testing

7/26/2019 Introduction to ADC Testing

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Introduction to ADCtesting IDefnition o basic parameters

Jn aliga

Dept. o Electronics and TelecommunicationsTechnical Uniersit! o "osice# $loa%ia


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Agenda Introduction Deterministic and probabilistic

models &asic static parameters &asic d!namic parameters 'ther parameters


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A(D conerter ) A(D

interace

ADC

A(D interace

Timing and control circuit

$ignalcondi*tioning

+eerence andpo,er sources

&u-er

$/0optional1

ADCx

=

Q

xroundk


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ADC parameters

0characteristics errors1 $tatic 02uasistatic1 parameters ) deried

rom transer characteristic

3oint 0gain# gain error# o-set# missing code# ...1 4unction 0transer characteristic# I56# D56# ...1 D!namic parameters ) characteri7e a

behaior o ADC at time*ar!ing signals $I5AD# E5' $5+# $4D+# T/D# I8D# ...

ADC parameter testing re2uirese9traordinaire accurac! E.g.: ; ?uncertaint! o

measurement = ;(0;@@B@1 @#@@@G


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Accurac! ersus precision


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ADC transer characteristicInputcode k

@;;

@;@

@@;

@@@

;;;

;;@

;@;

;@@ *B *H *< *;@ ; < H B

Inputanaloguealuex0t1

Vfs(Q

IdealADC+ealADC

Gain (slope)error

8issingcode

Error in monotonicity

Non-linearity

Offseterror

Ideal andreal straightlines

Vfs* ull scale rangeVfs= Vref(2

N-1)/(2N)

[ ] [ ]( ) QTTV NnomNnomNN

fsn =

= 2112

22

2

T[k] * transition leel0thresholdo code k1#W

[k]G Tk* Tk-1 ) codebin ,idth

N) nominal resolution0number o bi

ts1 o ADC

[ ] [ ]22

112

=

N

nomN

nomnom

TTQ


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Kain and o-set L their

errors 4itting the straight line:

End points straight line * connecting the

t,o end code transition or code midstepalues 6east*s2uare ft straight line according a

least*s2uare ftting algorithm

8inimum*ma9imum straight line * theline ,hich leads to the most positieand the most negatie deiations romthe ideal straight line


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ADC transer

characteristicDeterministic model Stochastic model

0 1 1,5 2

P(k|x)

1

Deterministic

definition

Stochastic

definition

1 2

101

100

Outputcode k

Inputanaloguevalue x(t)

Vfs!2N

"

Inputanaloguevalue x(t)

Vfs!2N

"

Channel profile

Outputcode k

analogueInput

alue x(t)

!Vfs"2N

#

$11

$1$

$$1

$$$

111

11$

1$1

1$$

- - -% & 2 -1 $ 1 2 & %

' N21$* -1

Conditionalprobabilit!

[ ] [ ]( ) ( ) [ ]( ) +$, ==< TESTTESTTESTTESTTEST kTkkPkTkkPkT


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D56 and I56 Di-erential non*linearit!

Integral non*linearit!

nom

nom

M

QkWkDNL

*G

nom

nom

M

kTkT

kINL

*G

[ ] [ ]

[ ] [ ]kDNLkINL

iDNLkINLk

i

+=

==

1

$


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D!namic parameters I Bandwidth0&N1 * the band o re2uencies o

input signal that the ADC under test is intended todigiti7e ,ith nominal constant gain. It is also

designated as the /al*po,er &and,idth# i.e.# there2uenc! range oer ,hich the ADC maintains ad!namic gain leel o at least H d& ,ith respect tothe ma9imum leel.

Gain fatness error0K0f11 * the di-erence

bet,een the gain o the ADC at a gien re2uenc!in the ADC band,idth# and its gain at a specifedreerence re2uenc!# e9pressed as a percentage othe gain at the reerence re2uenc!. The reerencere2uenc! is t!picall! the re2uenc! ,here theband,idth o ADC presents the ma9imum gain. 4or

DC*coupled ADCs the reerence re2uenc! isusuall f G @.


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Muantisation noise and

errors Caused b! rounding in 2uantisation process

0and ADC non*linearit!1

3o,er o 2uantisation noise or ideal ADC0


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ADC noise and distortion ADC output random noise) random signal:

Muantisation noise * uniorm 5oise generated in input analogue circuits * Kaussian

5oise caused b! sampling re2uenc! Pitter and apertureuncertaint! 0"oba!ashi1 Spurious) un,anted deterministic spectral

components uncorrelated ,ith input signal 0e.g.F@/71

Total noise) an! deiation bet,een the outputsignal 0conerted to input units1 and the inputsignal# e9cept deiations caused b! linear timeinariant s!stem response 0gain and phase shit1#harmonics o the undamental up to the re2uenc!fm# or a DC leel shit.

Distortion) ne, un,anted deterministic spectral


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5oise Qoor determines the lo,est input signal po,er

leel ,hich is reliabl! detectable at the ADC

output# i. e.# it limits the ultimate ADCsensitiit! to the ,ea% input signals# sincean! signal ,hose amplitude is belo, thenoise Qoor 0$5+ = @ d&1 ,ill become diRcultto recoer.

[ ]

ma

ma

12"

1

2

2

22

2

221

hh

hM

MYkY

NFl

M

hJkJkk=

+=

=


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D!namic parameters II

$ignal to noise and distortion ratio SINAD: or a pure sine,ae input o specifed

amplitude and re2uenc!# the ratio o the rmsamplitude o the ADC output undamental tone to

the rmsamplitude o the output noise# ,herenoise is defned as to include not onl! randomerrors but also non*linear distortion and thee-ects o sampling time errors# i.e.# the sum o allnon*undamental spectral components in the

range rom DC 0e9cluded1 up to hal the samplingre2uenc! 0fs/21. [ ]

[ ]

=

++

=

12"

1

222

22

22

12

log1$M

Jkk

d

MYNFl!Y

NFlJYSIN"D


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D!namic parameters III

$5+ $ignal to noise ratio 0$5+1 * harmonic

signal po,er 0rms1 to broadband noise

po,er ratio e9cluding DC# undamental#and harmonics

[ ]

[ ] ( )

=+++

=

12"

1

22

ma-

2

22

2211

log1$M

hJkJkk

d

MYNFlhkY

NFlJYSN#


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D!namic parameters IS

T/D# T/DLnoise# I8D T/D

T/DLnoise G ;($I5AD

Intermodulation distortion 0I8D1 * or an inputsignal composed o t,o or more pure sine,aes#

the distortion due to output components atre2uencies resulting rom the sum anddi-erence o all possible integer multiples o theinput re2uenc! tones.

"

$

T$D"

$

T$D i"D%i

i"D%i

d

==

22

log2$

IMton&

"IMD=


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D!namic parameters SE-ectie 5umber o &its

E-ectie 5umber o &its 0Nef# E5'&1 * or a sinusoidal inputsignal# Nefis defned as:

,here rmsis the rmstotal noise including harmonicdistortion and

eq

the ideal rms2uantisation noise or asinusoidal input. 0SINADdBSG SINADdB*


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Spurious-ree dynamic range (SFDR) -e9presses therange# in d o input signals l!ing bet,een the aeragedamplitude o the ADCs output undamental tone# f"# tothe aeraged amplitude o the highest re2uenc!

harmonic or spurious spectral component obsered oerthe ull 5!2uist band# or a pure sine,ae input ospecifed amplitude and re2uenc!# i.e.# m#x$%&(f')% %&(fs*)%+:

,here: ,mis the aeraged spectrum o the ADC output#f" is the input signal re2uenc!# f'and fs*are the

re2uencies o the set o harmonic and spurious spectralcomponents.

},

=0)(00)(ma-0

)(log2$)(

s'()mh()m

i()m

fYfY

fYdSFD#

D!namic parameters SI$4D+


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D!namic parameters SIIE9perimental demonstration

8easurement setup 0run generatorfrst and then demonstration1

5I U$& @@ADC: ;< bits# ;@%/7#

di-erential

AI; 0DUT1 U$&

$ot,are 06abSIEN1:

;. $ine,ae generator G $oundcard


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'ther parameters

Sarious electrical parameters# e.g.input impedance# po,er

re2uirements# grounding# Time parameters# e.g. cloc%

re2uenc!# conersion time#sampling re2uenc!#

Digital output: data coding# leels0logic1# serial(parallel# error bit rate#


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Introduction to ADCtesting II&asic standardi7ed test methods


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Agenda

$tandardi7ation $tatic test method /istogram test D!namic test ,ith data processing

in time domain D!namic test ,ith data processing

in spectral domain


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$tandardi7ation IEEE $td. ;@FV * ;B# WIEEE $tandard or Digiti7ing Naeorm

+ecordersW# IEEE $td. ;


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ADC static test

$tandardi7ed method


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ADC static test * basicideas

Xields ADC transer characteristic $tatic point and unction parameters

can be deried and calculated: Kain# o-set# 4$# D56# I56#

&ased on the stochastic model o ADC $imple test setup ) DC oltmeter is the

onl! accurate instrument Time consuming ) each Tk is

determined indiiduall!. The total time:


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$tatic test setup 0IEEE;@FV1

3rogramableDC source

+ecording deice#e.g. logic anal!7er

D!under

&u-er

Control and sampling

cloc%# ADC po,er# ...

Control of test stand03C1

DC

Soltmeter


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ADC static test * algorithm $tart ,ith the code k G ; 4ind an input oltage leel or ,hich the probabilit!

o codes lo,er than k in the record is slightl!

higher than @.F ) the oltage is belo, Tk. 4ind a bit higher oltage 0the usual step is a 2uarter

o Q1 or ,hich the probabilit! o codes lo,er than kis slightl! lo,er than @.F ) the oltage is aboe Tk

4it these t,o point b! line and calculate the oltageor ,hich the probabilit! o codes smaller than [email protected] ) this is the transition leel o code k ) theoltage e2ual to Tk

+epeat the procedure or all k G ;#


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Uncertaint! in the statictest

The uncertaint! can be reduced b!increasing the number o ac2uired samples

01. The table sho,s the measurement precision

or a confdence leel o #YV>.5umber o ac2uired samples01

B o noise standarddeiation1

BF> ; >


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The main disadantageo the static testing

The test is long time consuming: 6et]s test ;bit ADC ,ith sampling

re2uenc! ;@%/7# testing step is M(B#additie noise: G;6$ re2uired precision:better than ;@>.

The chosen record length:


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$tatic testE9perimental demonstration

8easurement setup 0run demonstration1

5I U$& @@ADC: ;< bits# ;@%/7#

di-erentialDAC: ;< bit# static# +$E

AI@ 0DUT1

AI; 0Soltmeter1

A'@ 0DCsource1

U$&

;:;@

$ot,are 06abSIEN1 controls:

;. A'@ G DC test oltage


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Alternatie static method,ith eedbac% * IEEE ;


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Alternatie static method,ith eedbac% * IEEE ;


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I5I U$& @@Y 0;< bits# ;@%/7#;@@@@s(T1

ome e per men a resu s


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ome e9per men a resu sII5I U$& @@Y( 0;@@@@s(T1

Di-erence ot,o

ollo,ingmeasurements

$,itchingmonitorduring themeasuremen

t


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/istogram 0statistical1test

$tandardi7ed method


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/istogram 0statistical1 test&asic ideas I

Koal: to determine ADC transercharacteristic 0the same as in static testmethod1

The calibrating signal is a time inariantrepetitie signal coering the ADC ull scale The stream o ADC output codes is recorded /istogram is built rom the record

The relatie count o hits in code bin k in thehistogram in comparison to the calibratingsignal probabilit! densit! unction 0or counts orcode bink in cumulatie histogram in relation tosignal probabilit! distribution unction1 giesinormation about the code bin ,idth 0or codetransition leels1


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/istogram 0statistical1 test&asic ideas II

The best shape ,ould be ramp or triangularsignal. Nh!O3roblemO

The basic recommended signal b! allstandards: sine,ae. Nh!O To achiee a re2uired accurac! a relatie

long record 0or records1 is re2uired

4aster than the static test +e2uirement: an accurate generator ,ith

an e9tremel! high accurac! 0lo, distortion#high linearit!# high spectral purit!1


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/istogram 0statistical1 testKeneral test setup

"ecordingde#ice

D! undertest

Bu$er

!%&generator

!ontrol and dataprocessing ('!)

Synchronisation

otchlter

ccurate generator(ar*itrary+ DDS)

'bliged+ecommended'ptional


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+amp signal 0IEEE ;


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$ine,ae signal0All standards1 ) theoretical bac%ground I

$ignal: Densit!

o probabilit!: Distribution o probabilit!:

( ) ( ) += ft"tx 2cos

( )22

1arccos

2

1

d

d2

x""

x

x

x'

=

=

[ ] ( )( )

( )

( ) ( )( )

2

21arcsin

2

2arcsin

1

d1

11

2

2

2

2122

1

1

1

=

==

N

Nfs

N

Nfs

kV

kV

"

kV

"

kV

xx"

kP

N

Nfs

N

Nfs

$ine,ae signal


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$ine,ae signal0All standards1 ) theoreticalbac%ground I

Ideal theoretical histogram:

D56:

Transition leels:

[ ] ( ) ( )( )

=

N

Nfs

N

Nfs

id "

kV

"

kVMk$

2

21arcsin

2

2arcsin

11

[ ] [ ] [ ]

[ ]k$k$k$

kDNLid

id=

[ ] [ ]

[ ] ( )1221

12

1cos =

= NN

,

, kfor$

k$"%kT

$ine,ae signal


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$ine,ae signal0All standards1 ) theoreticalbac%ground II

3roblem in pra9is: ,hat are thesine,ae parameters ) A# C ?6"dkO

Sarious ,a!s o estimation# e.gD!nad:

Incorrect

estimation?error ingain ando-set

[ ] [ ][ ]

[ ] [ ]

[ ][ ]

[ ]

[ ]

[ ][ ] [ ][ ]

[ ][ ][ ]12

22cos

12

$cos

14

124

4

12

22

cos12

$

cos

12

22cos1

4

12

$cos12

4

4

+

=

+

=

N%

N%

N%

%

N

N%

N%

N%

%

N%

N%

N%

%N

$

$

$

$

TT"

$

$

$

$

$

$T

$

$T

%


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$ine,ae signalTest conditions I

The total record must contain e9actl! aninteger number7o sine,ae c!cles

!partial records can be used instead o onelong record Total recorded number 8 o samples must

be relatiel! prime ,ith J# i.e. the! hae no

common actor Then the sampling andsine,ae re2uenc! are:

si fMJf =

si ffrJMr

r=

2

1


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$ine,ae signalTest conditions II

The number o samples 01 to ac2uire inthe histogram test# depends on: The noise leel in the measurement s!stem# The re2uired tolerance 0Bis measured in 6$&s1

and confdence leel 01 and the is di-erent iD56 02uanti7ation interal1 or I56 0transitionleels1 it to be determined.

The specifcation o tolerance or an indiidualtransition leel or code bin ,idth# or or the,orst case in all range.

( ) =+ 1QTTQTP ME"Sr&(lME"S


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$ine,ae signalTest conditions III

The e2uation generall! used to determine the number orecords to ac2uire is:

7G; or I56#7G< or D56# is the standard deiation o noiseleel in olt or the I56 determination and the smaller othe alues o and Q(;#; or the D56 determination.

[ ] [ ]

[ ] [ ]

( )

d&!

MTT

V,

,TT,

!

J#

NS

N

N

==

+=

+

=

$

1

21

22erf2

11221

2$11211

2


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$ine,ae signal$imulation

$imulation G 0see the simulation1: 4orm o histogram or arious test

signals Error caused b! limited number o

samples Error caused non*coherent sampling Error caused b! noise in input signal Error caused b! higher harmonics
http://var/www/apps/conversion/tmp/scratch_2/examples/Histogram%20simulation.vihttp://var/www/apps/conversion/tmp/scratch_2/examples/Histogram%20simulation.vi


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/istogram testE9perimental demonstration

8easurement setup 0run generatorfrst and then demonstration1

5I U$& @@ADC: ;< bits# ;@%/7#

di-erential

AI; 0DUT1 U$&;:

Introduction to ADC Testing

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Transcript of Introduction to ADC Testing