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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