Testing of AD Converters Istvn Kollr Budapest University

Testing of A/D Converters István Kollár Budapest University of Technology and Economics Dept. of Measurement and Information Systems Budapest, Hungary

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 • Lab. View • MATLAB • Summary Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 2

Input signals • Paradox: determine signal from erroneous data… • Solution: parametric model: • sine wave • exponential • ramp Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 3

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 TC 4) Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 4

Location of Code Transitions Direct measurement: feedback loop Histogram – of what? Ramp vs. sine wave Nonlinearity Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 5

DFT/FFT Test Sine wave Coherent sampling Total harmonic distortion Spurious-free dynamic range Intermodulation distortion Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 6

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 Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 7

Causes of Ambiguity • • • Starting values Iteration details Stop criteria Number representation Numerical algorithms (roundoff) Written standard + standard program(s) vs. detailed standard Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 8

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) Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 9

3 -parameter Fit Linear in A, B, C: LS solution of where is known. Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 10

4 -p Fit: Starting Values Nonlinear in • Choice of is optional in the standard • Maximum of DFT ( /2) • Count zero crossings (min. 5 periods) • Interpolated FFT Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 11

Algorithm I. Minimize vs. , A, B, C Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 12

Algorithm II. Algorithm: recursively find LS solution for xi of Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 13

Algorithm III. Newton-Raphson method Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 14

Algorithm IV. Newton-Gauss method Advantage: Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 15

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 Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 16

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 Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 17

Candidate Programs · · · · MATLAB Lab. View Lab. Windows Agilent VEE Geni. DAQ MATRIXx Scilab Mathematica Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 18

Sources of Program Information MATLAB, URL: http: //www. mathworks. com/ Lab. View, URL: http: //www. ni. com/labview/ Lab. Windows, URL: http: //www. ni. com/cvi/ VEE, URL: http: //www. home. agilent. com/ Geni. DAQ, URL: http: //www. advantech. com/support/detail_list. asp? model_id=Geni. DAQ MATRIXx, URL: http: //www. ni. com/matrixx/ Scilab, URL: http: //www. scilab. org/ Mathematica, URL: http: //www. wolfram. com/ Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 19

Labview Programs Aim: support IEEE-STD-1057 • Original Lab. View source • New: stand-alone programs for PC and Macintosh Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 20

Labview Program Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 21

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 Lab. View is good, but Matlab is also required Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 22

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 Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 23

The Framework • Standard mode • Curve fitting, DFT and other standardized methods, support automatic processing • Graphical mode • For visual evaluations • Compatible mode • Compatible with the Lab. View program • Advanced, development mode • Test-bed for new ideas Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 24

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) Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 25

The Program Page http: //www. mit. bme. hu/projects/adctest/ Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 26

The Program Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 27

Data Files Common for Programs Page: http: //www. mit. bme. hu/projects/adctest Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 28

Summary • The framework • Standard, precise calculations • Flexible interfaces for different purposes • Future work • Version 3. 2 will soon on the internet: http: //www. mit. bme. hu/projects/adctest/ • Continuous development • Interactive environment • Ideas and comments are appreciated Summer School on ADC and DAC June-July 2006 István Kollár Budapest University of Technology and Econ. 29