Brownian-Bridge-Based Statistical Analysis of the DAC INL Caused by Current Mismatch

This brief analytically investigates the digital-analog converter (DAC) integrated nonlinearity (INL) with respect to the accuracy of the DAC unit elements. The main novelty of the presented approach is in the application of the Brownian Bridge (BB) process to precisely describe the INL. This method...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 2, Analog and digital signal processing Analog and digital signal processing, 2007-02, Vol.54 (2), p.146-150
Main Authors: Radulov, G.I., Heydenreich, M., van der Hofstad, R.W., Hegt, J.A., van Roermund, A.H.M.
Format: Article
Language:English
Subjects:
Architecture
Bridges
Brownian Bridge (BB)
Chip formation
Chips
Circuits
Deviation
Digital-analog conversion
digital-analog converter (DAC)
integrated nonlinearity (INL)
Linearity
Mathematical analysis
mismatch
Monte Carlo methods
Probability density function
Probability density functions
Production
Random variables
Silicon
static linearity
Statistical analysis
Studies
Terrorism
Thermometers
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Summary:This brief analytically investigates the digital-analog converter (DAC) integrated nonlinearity (INL) with respect to the accuracy of the DAC unit elements. The main novelty of the presented approach is in the application of the Brownian Bridge (BB) process to precisely describe the INL. This method analyzes the thermometer and binary DAC architectures and is the first to prove that their statistical INL properties are different. The INL of the thermometer DAC is represented as a one-dimensional BB process. For the binary case, the INL is represented as combinations of random variables, the increments of which coincide with a BB process. For both architectures, this brief derives formulas for the INL main statistical properties, e.g., probability density function, mean, deviation, and chip yield. These properties are compared with previous analytical attempts and conclusions are drawn. The results of this brief fill a gap in the general understanding of the most quoted DAC specification- the INL. In particular, for a high-volume chip production, the derived formulas will help engineers to choose the DAC architecture and the allowed mismatch of the DAC unit elements
ISSN:1549-7747
1057-7130
1558-3791
DOI:10.1109/TCSII.2006.886900