Testing of A/D Converters

István Kollár

Budapest University of Technology and Economics

Dept. of Measurement and Information Systems

Budapest, Hungary

István KollárBudapest University of Technology and Econ. 2

Summer School on ADC and DACJune-July 2006

Outline

• Dynamic measurements: what is the input?• Standards

• Standardization projects, advantages and problems

• Main test methods• Sine wave fit: 3-parameter vs. 4-parameter• 4-parameter fit

• Starting values• Algorithm

• Programs• LabView• MATLAB

• Summary

István KollárBudapest University of Technology and Econ. 3

Summer School on ADC and DACJune-July 2006

Input signals

• Paradox: determine signal from erroneous data…

• Solution: parametric model:• sine wave• exponential• ramp

István KollárBudapest University of Technology and Econ. 4

Summer School on ADC and DACJune-July 2006

Standardization Projects• IEEE 1057-1994 (standard for digitizing

waveform recorders)• IEEE 1241-2000 (standard for terminology

and test methods for analog-to-digital converters)

IEC

• DYNAD – dynamic characterization and testing of analogue to digital converters

• EUPAS – European project for ADC-based devices standardization (in IMEKO TC4)

István KollárBudapest University of Technology and Econ. 5

Summer School on ADC and DACJune-July 2006

Location of Code Transitions

Direct measurement: feedback loop

Histogram – of what?

Ramp vs. sine wave

Nonlinearity

István KollárBudapest University of Technology and Econ. 6

Summer School on ADC and DACJune-July 2006

DFT/FFT Test Test

Sine wave

Coherent sampling

Total harmonic distortion

Spurious-free dynamic range

Intermodulation distortion

István KollárBudapest University of Technology and Econ. 7

Summer School on ADC and DACJune-July 2006

Sine Wave Fitting

IEEE 1241-2000 (standard for terminology and test methods for analog-to-digital converters)• Sine wave fitting

Problems: detailed description, but• Complex algorithms using computer• One-step and/or iterative solutions• Non-defined or partly defined details• Not always repeatable results

István KollárBudapest University of Technology and Econ. 8

Summer School on ADC and DACJune-July 2006

Causes of Ambiguity

• Starting values• Iteration details• Stop criteria• Number representation• Numerical algorithms (roundoff)

Written standard + standard program(s)

vs. detailed standard

István KollárBudapest University of Technology and Econ. 9

Summer School on ADC and DACJune-July 2006

3-parameter vs. 4-parameter Fit

• 3-parameter:• Frequency ratio must be exactly known• Linear in the parameters (one-step solution)

• 4-parameter:• More robust• Works also when the frequency ratio is exactly

known• Non-linear in the parameters (iterative solution)

István KollárBudapest University of Technology and Econ. 10

Summer School on ADC and DACJune-July 2006

3-parameter Fit

Linear in A, B, C

A, B, C: LS solution of

where is known.

2M

1=n

2nnn )(min C - )tBsin( - )tAcos( -ymin xDy

xDy )(

0

C

B

A

x

István KollárBudapest University of Technology and Econ. 11

Summer School on ADC and DACJune-July 2006

4-p Fit: Starting ValuesNonlinear in • Choice of is optional in the standard

• Maximum of DFT ( /2)• Count zero crossings (min. 5 periods)• Interpolated FFT

István KollárBudapest University of Technology and Econ. 12

Summer School on ADC and DACJune-July 2006

Algorithm I.

Minimize vs. , A, B, C

M

1=n

2nnn C - )tBsin( - )tAcos( -y

István KollárBudapest University of Technology and Econ. 13

Summer School on ADC and DACJune-July 2006

Algorithm II.

Algorithm: recursively find LS solution for xi of

i

i

i

i

i C

B

A

x

MiMiMiMiMiMi

iiiiii

iiiiii

i

ttBttAtt

ttBttAtt

ttBttAtt

111111

212121212121

111111111111

1

cossin1sincos.

.

.

.

.

. cossin1sincos

cossin1sincos

D

ii xDy )( 1

István KollárBudapest University of Technology and Econ. 14

Summer School on ADC and DACJune-July 2006

Algorithm III.

Newton-Raphson method

...)(

2

1)()()(

2

2

pp

ppp

p

pppp T KK

KK

p

p

p

p

p

p

pp

p

2

T

p

T

p

KKδK 2

0

T

p

p

p

pp

)()(

1

2

2 KK

István KollárBudapest University of Technology and Econ. 15

Summer School on ADC and DACJune-July 2006

Algorithm IV.

Newton-Gauss method

Advantage:

0)()()()(

1

2

2

T

p

p

p

p

p

pp

p

p KKKK

11T

1

1

1T

1

1

2

2 )()(

iiiiii xy

KKDDDD

p

p

p

pxp

T

yiiiiiiT

1

1

1T

11

DDDxxx

01

1

1

1i

i

i

i C

B

A

x

i

i

i

i

i C

B

A

x

István KollárBudapest University of Technology and Econ. 16

Summer School on ADC and DACJune-July 2006

Algorithm V.

Difficulty: Nothing guarantees decrease of cost function

when applying step (second-order approximation)

Stop criterion?

Good news: In practice cf almost always decreases,

especially if at least 5 periods were measured

István KollárBudapest University of Technology and Econ. 17

Summer School on ADC and DACJune-July 2006

Stop Criteria

Stop if error is small enough (?): Largest possible step is already small Step below noise level Step below noticeable error Step below roundoff error

Display: significant bits only

István KollárBudapest University of Technology and Econ. 18

Summer School on ADC and DACJune-July 2006

Candidate Programs

MATLAB LabView LabWindows Agilent VEE GeniDAQ MATRIXx Scilab Mathematica

István KollárBudapest University of Technology and Econ. 19

Summer School on ADC and DACJune-July 2006

Sources of Program Information

MATLAB, URL: http://www.mathworks.com/

LabView, URL: http://www.ni.com/labview/

LabWindows, URL: http://www.ni.com/cvi/

VEE, URL: http://www.get.agilent.com/gpinstruments/products/vee/support/

GeniDAQ, URL: http://www.advantech.com/products/GeniDAQ%20for%20Windows%20CE.asp

MATRIXx, URL: http://www.windriver.com/products/html/matrixx.html

Scilab, URL: http://www-rocq.inria.fr/scilab/scilab.html

Mathematica, URL: http://www.wolfram.com/

István KollárBudapest University of Technology and Econ. 20

Summer School on ADC and DACJune-July 2006

Labview Programs

Aim: support IEEE-STD-1057 • Original LabView source• New: stand-alone programs for PC and

Macintosh

István KollárBudapest University of Technology and Econ. 21

Summer School on ADC and DACJune-July 2006

Labview Program

István KollárBudapest University of Technology and Econ. 22

Summer School on ADC and DACJune-July 2006

General Requirements for a Program

• Theoretical• Accurate and fast realization• Careful documentation of the standard algorithms

• Practical• Known environment• User-friendly and flexible interface• Availability (via internet)• Interactivity

LabView is good, but Matlab is also required

István KollárBudapest University of Technology and Econ. 23

Summer School on ADC and DACJune-July 2006

Why MATLAB?

• Available for several platforms in many labs and universities

• IEEE double-precision numbers (64 bit)• Matrix, vector processing oriented (including

DFT), implemented in C• Easy to examine and extend the code• User-interface support• Negligible cross-platform compatibility

problems

István KollárBudapest University of Technology and Econ. 24

Summer School on ADC and DACJune-July 2006

The Framework

• Standard mode• Curve fitting, DFT and other standardized

methods, support automatic processing

• Graphical mode• For visual evaluations

• Compatible mode• Compatible with the LabView program

• Advanced, development mode• Test-bed for new ideas

István KollárBudapest University of Technology and Econ. 25

Summer School on ADC and DACJune-July 2006

Interfaces

• User interface• Graphical user interface• Self-documentation to support repeatability• ASCII file format to modify the settings easily

• I/O interface• Several input file format supporting (ASCII, wave,

custom)• Different output files (ASCII, mat, custom)

István KollárBudapest University of Technology and Econ. 26

Summer School on ADC and DACJune-July 2006

The ProgramPage http://www.mit.bme.hu/services/ieee/ADC-test/

István KollárBudapest University of Technology and Econ. 27

Summer School on ADC and DACJune-July 2006

The Program

István KollárBudapest University of Technology and Econ. 28

Summer School on ADC and DACJune-July 2006

Data Files (Common for Programs)

Page: http://www.mit.bme.hu/services/ieee/ADC-test/data/

István KollárBudapest University of Technology and Econ. 29

Summer School on ADC and DACJune-July 2006

Summary

• The framework• Standard, precise calculations• Flexible interfaces for different purposes

• Future work• Version 3.1 is on the internet:

http://www.mit.bme.hu/services/ieee/ADC-test/• Continuous development• Interactive environment• Ideas and comments are appreciated