⚡ electrical engineering

A Data-Driven Approach for Indirect Estimation of INLmax_abs Using Dynamic Parameters as Input Features

This paper proposes a data-driven indirect estimation method for INLmax_abs that utilizes dynamic parameters as input features within a Hybrid KNN-SVR machine learning model, achieving high accuracy and robustness across multiple ADC datasets while significantly improving testing efficiency compared to traditional code-density histogram approaches.

Original authors: Rongjie Li, Houjun Wang, Pu Pu, Jia Li, Guibing Zhu, Wanyu Yang

Published 2026-11-03

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Rongjie Li, Houjun Wang, Pu Pu, Jia Li, Guibing Zhu, Wanyu Yang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the vast ecosystem of modern electronics, the analog-to-digital converter acts as a critical translator. It takes the smooth, continuous waves of the real world—sound, light, temperature—and chops them into the discrete, binary steps that computers can understand. For these devices to function correctly, their translation must be precise. If the steps are uneven, the digital version of a sound wave will sound distorted, or a temperature reading will drift. Engineers measure this unevenness using a specific metric called integral nonlinearity. In simple terms, this metric reveals how much the device's actual behavior deviates from a perfect, straight line. The most important number in this measurement is the maximum absolute deviation, which tells us the worst-case error the device could produce.

For decades, finding this number has been a slow and expensive process. To measure it accurately, engineers must feed the device a perfect, slow-moving signal and record thousands, sometimes millions, of output points to build a statistical picture of its behavior. As devices have become faster and more complex, the time and equipment required for this testing have grown prohibitively large, creating a bottleneck in manufacturing. The question facing the industry has been whether there is a way to predict this worst-case error without running the full, time-consuming test.

A team of researchers from the University of Electronic Science and Technology of China has proposed a new approach to solve this problem. Instead of waiting for the slow, exhaustive test to finish, they suggest looking at the device's dynamic performance—how it reacts to a standard, fast-moving signal—to predict the static error. They treat the relationship between these two types of performance as a pattern that can be learned. By feeding a computer model data on how a device handles noise and distortion during a quick dynamic test, the model can estimate the maximum static error with surprising accuracy. This method does not replace the need for understanding the device's physics, but it offers a shortcut that could significantly speed up the testing of new chips.

The researchers began by gathering data from five different types of analog-to-digital converters, ranging from 8-bit to 16-bit resolution. These devices came from major manufacturers and used different internal designs. For each chip, they performed two distinct tests. First, they ran the traditional, slow test to get the true, ground-truth value of the maximum static error. Second, they ran a much faster dynamic test using a pure sine wave. From this quick test, they extracted several key numbers that describe the quality of the signal, such as the ratio of signal to noise and the level of harmonic distortion. These numbers served as the input features for their machine learning model.

The core of their work was building a model that could connect these quick dynamic numbers to the slow static error. They tested several different mathematical approaches, including standard methods used in data science and more complex deep learning networks. However, they found that the most effective solution was a hybrid model that combined two simpler techniques. One technique excels at looking at local neighbors in the data, while the other is better at understanding the overall shape of the data. By blending these two strengths, the model could adapt to the specific quirks of each different chip type, whether the data was spread out evenly or clustered in a specific way.

The results showed that this data-driven strategy works. When the researchers tested the model on chips it had not seen before, the predictions were remarkably close to the actual measurements. For the different chip types, the average error in the prediction ranged from roughly 0.03 to 0.21 units of the least significant bit, which is the smallest step the device can measure. In many cases, the model performed as well as or better than the more complex deep learning systems, despite using a much simpler structure. The model successfully learned that when a chip shows high levels of noise or distortion in a quick dynamic test, it is highly likely to have a larger static error as well.

The researchers also analyzed which specific numbers from the dynamic test were the most important for making the prediction. They found that the answer varied depending on the type of chip. For some devices, the total harmonic distortion was the strongest indicator, while for others, the combined ratio of signal to noise and distortion was the most reliable clue. This variation confirmed that no single number could tell the whole story for every chip, reinforcing the need for a model that could weigh multiple factors simultaneously. The study demonstrated that by combining these different dynamic parameters, the model could capture the complex relationship between the fast and slow behaviors of the device.

While the results are promising, the authors are careful to note the boundaries of their method. The model was trained and tested using low-frequency signals that covered the full range of the device's input. This means the approach is currently best suited for testing under these specific conditions and may not work as well if the device is used with very high-frequency signals or signals that do not fill the entire input range. Furthermore, the method is designed to estimate the maximum error, not to detect every single missing code or to replace the need for testing in all scenarios. It is a tool for rapid assessment, particularly useful in production lines where speed is essential and the manufacturing process is already well-understood.

This work represents a shift in how engineers might approach the quality control of electronic components. By showing that a quick dynamic test can reliably predict a slow static parameter, the researchers have opened the door to more efficient testing workflows. The hybrid model they developed proves that a combination of simple, complementary techniques can often outperform more complex systems, especially when dealing with the varied and sometimes messy data found in real-world manufacturing. As the demand for faster and more precise electronics continues to grow, such data-driven shortcuts may become an essential part of ensuring that the devices powering our world are both high-quality and available in time.

Technical Summary: A Data-Driven Approach for Indirect Estimation of INLmax_abs Using Dynamic Parameters as Input Features

Problem Statement
Accurate testing of Analog-to-Digital Converters (ADCs) is critical for ensuring product quality, yet the characterization of static parameters, specifically Integral Nonlinearity (INL), presents significant challenges in terms of time and cost. Traditional INL testing relies on code-density histogram methods using highly linear ramp or sinusoidal signals. As ADC resolution increases, the number of required samples grows exponentially to ensure sufficient code hits, leading to substantial test-time overhead and equipment costs. Furthermore, achieving high measurement accuracy often demands excitation signals with purity levels that exceed the capabilities of standard test equipment, introducing stimulus-induced errors. While existing strategies have attempted to optimize test stimuli or reduce sample counts through techniques like Fast Sine Wave Histogram Testing (FSHT) or wavelet reconstruction, many still require dedicated static test procedures or struggle to accurately capture high-frequency local variations in the INL curve. Consequently, there is a need for a method that can rapidly assess INL performance without the extensive data acquisition associated with traditional static testing.

Methodology
This paper proposes a data-driven, indirect estimation strategy for the maximum absolute value of INL ( $INL_{max\_abs}$ ). The core premise is that statistical correlations exist between an ADC's dynamic performance parameters and its static nonlinearity.

Feature Extraction: Instead of performing a full static INL test for every device, the method utilizes dynamic parameters extracted from standard spectral analysis of the ADC's output. The input features include Signal-to-Noise Ratio (SNR), Signal-to-Noise and Distortion Ratio (SINAD), Total Harmonic Distortion (THD), Spurious-Free Dynamic Range (SFDR), and individual harmonic components.
Data Acquisition: The study utilized test data from five distinct ADC datasets (ranging from 8-bit to 16-bit resolution, covering both SAR and Pipelined architectures) manufactured by Texas Instruments and Analog Devices. Static tests (using code-density histograms) provided the ground truth for $INL_{max\_abs}$ , while dynamic tests (using pure sine waves) provided the input features.
Model Construction: To address the variability in data distributions and sample sizes across different ADC types, the authors developed a Hybrid KNN-SVR model. This model integrates:
- k-Nearest Neighbors (KNN): Leveraged for its strong local fitting capability in densely populated regions of the feature space.
- Support Vector Regression (SVR): Leveraged for its robust global fitting capability, particularly effective in sparse regions.
- Adaptive Weighting: A sigmoid function dynamically adjusts the weighting coefficient ( $\alpha$ ) based on the local sample density ( $\delta$ ) of the input features. In dense regions, the model relies more on KNN; in sparse regions, it shifts reliance to SVR.
Validation: The proposed model was compared against standard machine learning algorithms, including standalone KNN, SVR, XGBoost, and Artificial Neural Networks (ANN). Performance was evaluated using $R^2$ , Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) on independent test sets derived from the five datasets.

Key Contributions

Statistical Correlation Discovery: The work establishes that dynamic parameters (SNR, SINAD, THD, SFDR) exhibit varying degrees of statistical correlation with $INL_{max\_abs}$ across different ADC architectures. While the strength of correlation varies by device, the combination of multiple dynamic parameters provides a robust basis for estimation.
Indirect Estimation Strategy: A data-driven framework is proposed that estimates $INL_{max\_abs}$ solely from dynamic test results, eliminating the need for a dedicated, high-sample-count static test stimulus for every device.
Hybrid KNN-SVR Model: The development of a lightweight hybrid model that outperforms or matches complex models like XGBoost and ANN. Crucially, this model demonstrates superior robustness across datasets with non-uniform distributions and varying sample sizes, a common challenge in production testing data.

Experimental Results
The proposed method was validated on five ADC datasets with sample sizes ranging from 682 to 1,507.

Accuracy: The Hybrid KNN-SVR model achieved RMSE values of 0.0532, 0.0607, 0.0301, 0.2006, and 0.2083 LSB across the five datasets, respectively.
Performance Comparison: The Hybrid model consistently outperformed the individual KNN and SVR base models. On four of the five datasets (AD0832, AD1674, AD7658, AD9245), it demonstrated performance comparable to or better than XGBoost and ANN. On the ADS8509 dataset, it performed comparably to these complex models.
Generalization: The model showed strong generalization capabilities, with estimated value distributions closely matching measured distributions in both training and test sets, indicating no significant overfitting.
Feature Importance: SHAP analysis revealed that the importance of specific features varies by device type. However, SINAD (which accounts for both noise and distortion) consistently emerged as a highly important feature across all datasets.

Significance and Limitations
The paper claims that this approach provides a valuable basis for the rapid assessment of INL performance, potentially reducing test time and data acquisition overhead in production environments by leveraging existing dynamic test data. The Hybrid KNN-SVR model offers a robust solution for scenarios involving small-to-medium datasets with non-uniform distributions.

The authors explicitly note several limitations:

Test Stimulus Constraints: The method relies on low-frequency, full-scale excitation. Its effectiveness at higher input frequencies or under non-full-scale conditions requires further validation.
Scope of Estimation: The method estimates $INL_{max\_abs}$ but does not currently address the indirect estimation of Differential Nonlinearity (DNL) or the detection of missing codes. Therefore, it is positioned as a supplementary estimation tool for well-validated manufacturing processes rather than a complete replacement for dedicated DNL or missing-code testing.
Device Range: Validation was limited to ADCs with sampling rates up to 50 Msps and resolutions up to 16 bits. Applicability to faster or higher-resolution devices remains to be investigated.

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