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

István Kollár Budapest University of Technology and Econ. 2 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 3 Summer School on ADC and DAC June-July 2006 Input signals Paradox: determine signal from erroneous data… Solution: parametric model: sine wave exponential ramp

István Kollár Budapest University of Technology and Econ. 4 Summer School on ADC and DAC June-July 2006 Standardization Projects IEEE (standard for digitizing waveform recorders) IEEE (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 Kollár Budapest University of Technology and Econ. 5 Summer School on ADC and DAC June-July 2006 Location of Code Transitions Direct measurement: feedback loop Histogram – of what? Ramp vs. sine wave Nonlinearity

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

István Kollár Budapest University of Technology and Econ. 7 Summer School on ADC and DAC June-July 2006 Sine Wave Fitting IEEE (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 Kollár Budapest University of Technology and Econ. 8 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 9 Summer School on ADC and DAC June-July 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 Kollár Budapest University of Technology and Econ. 10 Summer School on ADC and DAC June-July parameter Fit Linear in A, B, C A, B, C: LS solution of where  is known.

István Kollár Budapest University of Technology and Econ. 11 Summer School on ADC and DAC June-July 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

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

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

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

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

István Kollár Budapest University of Technology and Econ. 16 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 17 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 18 Summer School on ADC and DAC June-July 2006 Candidate Programs  MATLAB  LabView  LabWindows  Agilent VEE  GeniDAQ  MATRIXx  Scilab  Mathematica

István Kollár Budapest University of Technology and Econ. 19 Summer School on ADC and DAC June-July 2006 Sources of Program Information MATLAB, URL: LabView, URL: LabWindows, URL: VEE, URL: GeniDAQ, URL: CE.asp MATRIXx, URL: Scilab, URL: Mathematica, URL:

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

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

István Kollár Budapest University of Technology and Econ. 22 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 23 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 24 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 25 Summer School on ADC and DAC June-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 Kollár Budapest University of Technology and Econ. 26 Summer School on ADC and DAC June-July 2006 The Program Page

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

István Kollár Budapest University of Technology and Econ. 28 Summer School on ADC and DAC June-July 2006 Data Files (Common for Programs) Page: test/data/

István Kollár Budapest University of Technology and Econ. 29 Summer School on ADC and DAC June-July 2006 Summary The framework Standard, precise calculations Flexible interfaces for different purposes Future work Version 3.1 is on the internet: Continuous development Interactive environment Ideas and comments are appreciated