Optimal Design Method of Sub-Ranging ADC Based on Stochastic Comparator

Md. Maruf HOSSAIN  Tetsuya IIZUKA  Toru NAKURA  Kunihiro ASADA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.2   pp.410-424
Publication Date: 2018/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.410
Type of Manuscript: Special Section PAPER (Special Section on Analog Circuit Techniques and Related Topics)
sub-ranging ADC,  stochastic comparator,  yield,  probability density function,  optimization,  calibration,  

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An optimal design method for a sub-ranging Analog-to-Digital Converter (ADC) based on stochastic comparator is demonstrated by performing theoretical analysis of random comparator offset voltages. If the Cumulative Distribution Function (CDF) of the comparator offset is defined appropriately, we can calculate the PDFs of the output code and the effective resolution of a stochastic comparator. It is possible to model the analog-to-digital conversion accuracy (defined as yield) of a stochastic comparator by assuming that the correlations among the number of comparator offsets within different analog steps corresponding to the Least Significant Bit (LSB) of the output transfer function are negligible. Comparison with Monte Carlo simulation verifies that the proposed model precisely estimates the yield of the ADC when it is designed for a reasonable target yield of >0.8. By applying this model to a stochastic comparator we reveal that an additional calibration significantly enhances the resolution, i.e., it increases the Number of Bits (NOB) by ∼ 2 bits for the same target yield. Extending the model to a stochastic-comparator-based sub-ranging ADC indicates that the ADC design parameters can be tuned to find the optimal resource distribution between the deterministic coarse stage and the stochastic fine stage.