Advanced Strategies for Uncertainty-Guided Live Measurement Sequencing in Fast, Robust SAR ADC Linearity Testing

TL;DR

This work enhances Uncertainty-Guided Live Measurement Sequencing (UGLMS) for real-time SAR ADC linearity testing by introducing a rank-1 EKF update, a measurement-aligned covariance inflation, a low-order carrier polynomial extension, and a trace-based termination strategy. Collectively, these improvements yield up to 8× faster equal-accuracy INL/DNL reconstruction for 16-bit ADCs and sub-70 ms runtimes for 18-bit devices, while extending modeling capabilities to capture systematic nonlinearities and enabling robust, autonomous test termination. Simulations show full INL/DNL recovery in 36 ms for 16-bit and under 70 ms for 18-bit (120 ms with the polynomial extension), with 8× overall speedups when combined with the faster updates. Significance lies in real-time, production-ready SAR ADC linearity testing without full-range sweeps or offline post-processing, though some overhead remains at lower resolutions where baseline UGLMS may be preferable. Future hardware validation will translate these gains into practical production-test environments.

Abstract

This paper builds on our Uncertainty-Guided Live Measurement Sequencing (UGLMS) method. UGLMS is a closed-loop test strategy that adaptively selects SAR ADC code edges based on model uncertainty and refines a behavioral mismatch model in real time via an Extended Kalman Filter (EKF), eliminating full-range sweeps and offline post-processing. We introduce an enhanced UGLMS that delivers significantly faster test runtimes while maintaining estimation accuracy. First, a rank-1 EKF update replaces costly matrix inversions with efficient vector operations, and a measurement-aligned covariance-inflation strategy accelerates convergence under unexpected innovations. Second, we extend the static mismatch model with a low-order carrier polynomial to capture systematic nonlinearities beyond pure capacitor mismatch. Third, a trace-based termination adapts test length to convergence, preventing premature stops and redundant iterations. Simulations show the enhanced UGLMS reconstructs full Integral- and Differential-Non-Linearity (INL/DNL) in just 36 ms for 16-bit and under 70 ms for 18-bit ADCs (120 ms with the polynomial extension). Combining the faster convergence from covariance inflation with reduced per-iteration runtime from the rank-1 EKF update, the method reaches equal accuracy 8x faster for 16-bit ADCs. These improvements enable real-time, production-ready SAR ADC linearity testing.

Figures (5)

• Figure 1: Process flow of the original Uncertainty-Guided Live Measurement Sequencing (UGLMS) for SAR ADC linearity testing schey2025uncertainty. Highlighted blocks indicate aspects that are adapted and improved in this work.
• Figure 2: INL and DNL of a 12-bit ADC reconstructed after $200$ iterations with $M=64$ samples per local sweep and $1.0\,\mathrm{LSB}$ RMS measurement noise. A quadratic carrier term introduces a $1\,\mathrm{LSB}$ offset and non-uniform gain to model systematic nonlinearity. Each estimated curve (INL, DNL) is followed by its corresponding absolute error.
• Figure 3: Convergence of INLmax and DNLmax estimation error over $1000$ iterations for a 16-bit ADC with $1.0\,\mathrm{LSB}$ RMS measurement noise and $M=128$ samples per sweep. Both the uniform inflation method from schey2025uncertainty and the proposed measurement-aligned inflation were evaluated across $100$ runs. Mean error is shown with shaded envelopes marking the 10th and 90th percentiles.
• Figure 4: INLmax estimation error as a function of the NIS threshold $\tau$ and inflation factor $\alpha$ for a 16-bit ADC with $M=128$ samples per sweep and $1.0\,\mathrm{LSB}$ RMS noise. A total of 4725 parameter combinations ($\tau \in [0.01,0.25]$, $\alpha \in [1.1,20.0]$) were evaluated, each averaged over 20 independent simulation runs. The colormap spans a focused error range of $0.1-0.25\,\mathrm{LSB}$ to highlight regions of interest; deep blue indicates configurations with errors $\ge 0.25\,\mathrm{LSB}$.
• Figure 5: Final INLmax estimation error as a function of the termination threshold $\varepsilon$, using the criterion described in \ref{['secsub:TerminationStrategy']} with $N_\mathrm{term} = 12$, for a 16-bit ADC with $M=128$ samples per sweep and $1.0\,\mathrm{LSB}$ RMS noise. Each point corresponds to the result of $100$ independent runs, where a typical run (mean or 10th/90th percentile) terminates after a number of iterations determined by $\varepsilon$, yielding the corresponding INL error. For selected $\varepsilon$ values, bands indicate the full spread of errors across all 100 runs.