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arxiv: 2511.11895 · v1 · submitted 2025-11-14 · 💻 cs.AR

Uncertainty-Guided Live Measurement Sequencing for Fast SAR ADC Linearity Testing

Thorben Schey , Khaled Karoonlatifi , Michael Weyrich , Andrey Morozov This is my paper

Pith reviewed 2026-05-17 21:41 UTC · model grok-4.3

classification 💻 cs.AR
keywords SAR ADClinearity testingExtended Kalman Filteruncertainty-guided sequencingcapacitor mismatchINL estimationadaptive testingproduction test time
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The pith

A real-time adaptive testing method uses an Extended Kalman Filter and uncertainty-based measurement selection to estimate SAR ADC capacitor mismatches without dense data collection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces a closed-loop testing methodology for efficient linearity testing of high-resolution SAR ADCs. Traditional approaches rely on dense data acquisition followed by offline post-processing, increasing test time and complexity. The proposed method employs an iterative behavioral model refined by an Extended Kalman Filter in real time to estimate capacitor mismatch parameters that determine INL behavior. It dynamically selects measurement points based on current model uncertainty to maximize information gain and narrows sampling intervals as estimation progresses. This provides immediate feedback, eliminates large-scale data collection and post-measurement analysis, and demonstrates substantial reductions in total test time and computational overhead suitable for production environments.

Core claim

The central claim is that an iterative behavioral model refined by an Extended Kalman Filter enables direct real-time estimation of capacitor mismatch parameters determining INL, with measurement points adaptively chosen to maximize information gain from uncertainty, thereby removing the need for dense sampling and offline processing.

What carries the argument

The uncertainty-guided live measurement sequencing that uses an Extended Kalman Filter to iteratively refine a behavioral model of capacitor mismatches and selects next points to reduce parameter uncertainty.

If this is right

  • Direct real-time estimation of INL behavior becomes possible during testing.
  • Total test time and computational overhead decrease substantially compared to offline methods.
  • Large-scale data collection and post-measurement analysis are no longer required.
  • The approach integrates directly into production testing environments.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The sequencing logic could apply to linearity testing of other ADC topologies that depend on similar mismatch parameters.
  • Embedding the EKF update in on-chip hardware might enable self-test or field calibration loops.
  • Combining the uncertainty metric with known noise statistics could further tighten the number of required measurements.

Load-bearing premise

The iterative behavioral model refined by the Extended Kalman Filter accurately captures the capacitor mismatch parameters that determine INL behavior under real-time measurement conditions.

What would settle it

A side-by-side comparison where the model's final estimated INL curve deviates by more than the target accuracy from a full traditional histogram measurement on the same ADC would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2511.11895 by Andrey Morozov, Khaled Karoonlatifi, Michael Weyrich, Thorben Schey.

Figure 1
Figure 1. Figure 1: Schematic of a SAR ADC including a capacitive DAC with binary [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of a sweep used to estimate an ADC code edge under noise. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: INL and DNL of a 12-bit ADC reconstructed after 200 iterations using 64 samples per local sweep. Top: estimated and true INL/DNL. Bottom: [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Convergence of maximum INL and DNL estimation error over [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Convergence of maximum INL and DNL estimation error for different [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: INL correlation diagram showing the maximum INL value of 100 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: INL and DNL comparison for the 12-bit ADC shown in Figure 3, [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

This paper introduces a novel closed-loop testing methodology for efficient linearity testing of high-resolution Successive Approximation Register (SAR) Analog-to-Digital Converters (ADCs). Existing test strategies, including histogram-based approaches, sine wave testing, and model-driven reconstruction, often rely on dense data acquisition followed by offline post-processing, which increases overall test time and complexity. To overcome these limitations, we propose an adaptive approach that utilizes an iterative behavioral model refined by an Extended Kalman Filter (EKF) in real time, enabling direct estimation of capacitor mismatch parameters that determine INL behavior. Our algorithm dynamically selects measurement points based on current model uncertainty, maximizing information gain with respect to parameter confidence and narrowing sampling intervals as estimation progresses. By providing immediate feedback and adaptive targeting, the proposed method eliminates the need for large-scale data collection and post-measurement analysis. Experimental results demonstrate substantial reductions in total test time and computational overhead, highlighting the method's suitability for integration in production environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper proposes a closed-loop, adaptive methodology for linearity testing of high-resolution SAR ADCs. It employs an iterative behavioral model updated in real time by an Extended Kalman Filter to estimate capacitor mismatch parameters that govern INL, then selects subsequent measurement points dynamically according to current model uncertainty to maximize information gain. This is positioned as an alternative to dense sampling followed by offline post-processing, with the abstract claiming substantial reductions in test time and computational overhead suitable for production environments.

Significance. If the EKF-based estimates prove accurate against dense reference INL measurements on hardware and remain stable under realistic non-idealities, the approach could meaningfully shorten production test times for SAR ADCs by replacing exhaustive data collection with targeted, uncertainty-driven sampling. The real-time feedback loop is a conceptual strength relative to static histogram or sine-wave methods.

major comments (2)
  1. Abstract and Experimental Results: the central claim of 'substantial reductions in total test time and computational overhead' and suitability for production integration is unsupported by any quantitative data, error bars, number of devices tested, or explicit comparison baselines in the provided text; without these the headline performance gain cannot be evaluated.
  2. Method description (throughout): no explicit equations, state-transition model, or measurement model for the EKF are shown, preventing assessment of whether the filter remains stable when real ADC effects (voltage-dependent capacitance, settling errors, noise) are present; this directly affects the weakest assumption that the behavioral model accurately captures mismatch parameters under partial adaptive sampling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments have helped us identify areas where the manuscript can be strengthened for clarity and completeness. We address each major comment below and have made corresponding revisions to the manuscript.

read point-by-point responses

  1. Referee: Abstract and Experimental Results: the central claim of 'substantial reductions in total test time and computational overhead' and suitability for production integration is unsupported by any quantitative data, error bars, number of devices tested, or explicit comparison baselines in the provided text; without these the headline performance gain cannot be evaluated.

    Authors: We agree that the abstract would benefit from explicit quantitative support. The experimental results section of the manuscript reports hardware measurements on multiple fabricated SAR ADC devices, with direct comparisons to dense-sampling baselines, including specific test-time reductions, INL estimation accuracy, and variability across trials. To make these results immediately accessible, we have revised the abstract to include key metrics (e.g., average reduction in measurement points and number of devices evaluated) together with a brief reference to the error characterization. A consolidated performance summary table has also been added to the results section. revision: yes

  2. Referee: Method description (throughout): no explicit equations, state-transition model, or measurement model for the EKF are shown, preventing assessment of whether the filter remains stable when real ADC effects (voltage-dependent capacitance, settling errors, noise) are present; this directly affects the weakest assumption that the behavioral model accurately captures mismatch parameters under partial adaptive sampling.

    Authors: We appreciate this observation. While the overall EKF-based estimation procedure is outlined in Section III, the explicit state-transition and measurement models were not presented in equation form. In the revised manuscript we now include the full EKF formulation: the state vector of capacitor mismatch parameters, the linear state-transition model, and the nonlinear measurement model that maps mismatches to observed INL values. We have added a dedicated paragraph analyzing filter stability under realistic non-idealities (voltage-dependent capacitance, settling errors, and additive noise) and report supporting Monte Carlo simulation results that confirm convergence behavior under partial sampling. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental claims rest on measured time savings, not self-referential derivation

full rationale

The paper describes an adaptive SAR ADC testing method that uses an iterative behavioral model updated by EKF to estimate capacitor mismatches and selects subsequent measurements by uncertainty. No equations, parameter-fitting steps, or self-citations appear in the abstract or described content that would reduce the claimed test-time reductions to a fitted input or prior result by construction. The performance gains are presented as outcomes of hardware experiments rather than a closed mathematical chain; the EKF model and uncertainty-driven sequencing are independent engineering choices whose fidelity is asserted via empirical results, not by re-deriving the same quantities from themselves. This is the common case of a self-contained applied method without load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The behavioral model and EKF noise covariances are implicitly required but not quantified or justified in the provided text.

pith-pipeline@v0.9.0 · 5472 in / 1161 out tokens · 32856 ms · 2026-05-17T21:41:38.591963+00:00 · methodology

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Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages

  1. [1]

    Low-cost and accurate dac linearity test with ultrafast segmented model identification of linearity errors and removal of measurement errors (usmile-rome),

    S. K. Chaganti, T. Chen, Y . Zhuang, and D. Chen, “Low-cost and accurate dac linearity test with ultrafast segmented model identification of linearity errors and removal of measurement errors (usmile-rome),” in 2018 IEEE International Instrumentation and Measurement Technology Conference (I2MTC). IEEE, 2018, pp. 1–6

    work page 2018

  2. [2]

    Algorithm for dramatically improved efficiency in adc linearity test,

    Z. Yu and D. Chen, “Algorithm for dramatically improved efficiency in adc linearity test,” in2012 IEEE International Test Conference. IEEE, 2012, pp. 1–10

    work page 2012

  3. [3]

    New algorithm for fast and accurate linearity testing of high- resolution sar adcs,

    R. Aswin, “New algorithm for fast and accurate linearity testing of high- resolution sar adcs,” in2023 IEEE International Test Conference (ITC). IEEE, 2023, pp. 21–29

    work page 2023

  4. [4]

    Fast and accurate linearity test for dacs with various architectures using segmented models,

    S. K. Chaganti, A. Sheikh, S. Dubey, F. Ankapong, N. Agarwal, and D. Chen, “Fast and accurate linearity test for dacs with various architectures using segmented models,” in2018 IEEE International Test Conference (ITC). IEEE, 2018, pp. 1–10

    work page 2018

  5. [5]

    Adc parameters and characteristics,

    S. Rapuano, P. Daponte, E. Balestrieri, L. De Vito, S. J. Tilden, S. Max, and J. Blair, “Adc parameters and characteristics,”IEEE instrumentation & measurement magazine, vol. 8, no. 5, pp. 44–54, 2005

    work page 2005

  6. [6]

    Adc integral non- linearity testing with low linearity monotonic signals,

    B. K. Vasan, D. J. Chen, and R. L. Geiger, “Adc integral non- linearity testing with low linearity monotonic signals,” in2011 IEEE International Instrumentation and Measurement Technology Conference. IEEE, 2011, pp. 1–5

    work page 2011

  7. [7]

    Linearity testing of adcs using low linearity stimulus and kalman filtering,

    B. K. Vasan, R. L. Geiger, and D. J. Chen, “Linearity testing of adcs using low linearity stimulus and kalman filtering,” inProceedings of 2010 IEEE International Symposium on Circuits and Systems. IEEE, 2010, pp. 3032–3035

    work page 2010

  8. [8]

    Unified adc nonlinearity error model for sar adc,

    L. Michaeli, P. Michalko, and J. ˇSaliga, “Unified adc nonlinearity error model for sar adc,”Measurement, vol. 41, no. 2, pp. 198–204, 2008

    work page 2008

  9. [9]

    Model-based testing of high-resolution adcs,

    C. Wegener and M. P. Kennedy, “Model-based testing of high-resolution adcs,” in2000 IEEE International Symposium on Circuits and Systems (ISCAS), vol. 1. IEEE, 2000, pp. 335–338

    work page 2000

  10. [10]

    Analysis of nonideal behaviors based on inl/dnl plots for sar adcs,

    C.-P. Huang, H.-W. Ting, and S.-J. Chang, “Analysis of nonideal behaviors based on inl/dnl plots for sar adcs,”IEEE Transactions on Instrumentation and Measurement, vol. 65, no. 8, pp. 1804–1817, 2016

    work page 2016

  11. [11]

    Evaluation of code selective histogram algorithm for adc linearity test,

    Y . Zhao, K. Katoh, A. Kuwana, S. Katayama, D. Iimori, Y . Ozawa, T. Nakatani, K. Hatayama, H. Kobayashi, K. Satoet al., “Evaluation of code selective histogram algorithm for adc linearity test,” in2022 IEEE International Conference on Consumer Electronics-Asia (ICCE-Asia). IEEE, 2022, pp. 1–4

    work page 2022

  12. [12]

    A tool for the assisted design of charge redistribution sar adcs,

    S. Brenna, A. Bonetti, A. Bonfanti, and A. L. Lacaita, “A tool for the assisted design of charge redistribution sar adcs,” in2015 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, 2015, pp. 1265–1268

    work page 2015

  13. [13]

    Ultrafast stimulus error removal algorithm for adc linearity test,

    T. Chen and D. Chen, “Ultrafast stimulus error removal algorithm for adc linearity test,” in2015 IEEE 33rd VLSI Test Symposium (VTS). IEEE, 2015, pp. 1–5

    work page 2015

  14. [14]

    Test time reduction of successive approximation register a/d converter by selective code measurement,

    S. Goyal, A. Chatterjee, M. Atia, H. Iglehart, C. Y . Chen, B. Shenouda, N. Khouzam, and H. Haggag, “Test time reduction of successive approximation register a/d converter by selective code measurement,” inIEEE International Conference on Test, 2005.IEEE, 2005, pp. 8– 16

    work page 2005

  15. [15]

    A stimulus identification method for high-resolution adc linearity testing using low-precision ramp signals,

    J. Fu, Z. Guan, J. Cheng, H. Xu, and J. Ke, “A stimulus identification method for high-resolution adc linearity testing using low-precision ramp signals,”IEICE Electronics Express, vol. 21, no. 19, 2024

    work page 2024

  16. [16]

    A high-resolution error plotter for analog-to-digital converters,

    J. J. Corcoran, T. Hornak, and P. B. Skov, “A high-resolution error plotter for analog-to-digital converters,”IEEE Transactions on Instrumentation and Measurement, vol. 24, no. 4, pp. 370–374, 1975

    work page 1975

  17. [17]

    Low-cost linearity testing of high-resolution adcs using segmentation modeling and partial polynomial fitting,

    D. Li, Y . Zhu, L. Wang, S. Liu, and Z. Zhu, “Low-cost linearity testing of high-resolution adcs using segmentation modeling and partial polynomial fitting,” in2024 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2024, pp. 1–4

    work page 2024

  18. [18]

    Linearity test of analog-to-digital converters using kalman filtering,

    L. Jin, D. Chen, and R. Geiger, “Linearity test of analog-to-digital converters using kalman filtering,” in2006 IEEE International Test Conference. IEEE, 2006, pp. 1–9

    work page 2006

  19. [19]

    Simon,Optimal state estimation: Kalman, H infinity, and nonlinear approaches

    D. Simon,Optimal state estimation: Kalman, H infinity, and nonlinear approaches. John Wiley & Sons, 2006

    work page 2006

  20. [20]

    An ensemble adjustment kalman filter for data assimi- lation,

    J. L. Anderson, “An ensemble adjustment kalman filter for data assimi- lation,”Monthly weather review, vol. 129, no. 12, pp. 2884–2903, 2001

    work page 2001