ADC Gain Error Calibration Using Piecewise Linear Modeling
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Solution Overview
Problem
Existing methods for gain-error compensation in analog-to-digital converters (ADCs) fail to adequately address non-linearities and variances within the operating range, leading to significant accuracy degradation in precision analog-to-digital conversion systems.
Innovation Solution
Utilizing a digital-to-analog converter (DAC) with known low gain error and integral non-linearity characteristics to generate equally spaced analog voltage levels, which are sampled by the ADC, and employing piecewise linear basis functions to model and quantify gain error, allowing for precise compensation through least-squares analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional gain-error compensation methods are used in ADCs, then the device complexity is reduced, but the measurement precision deteriorates due to inadequate addressing of non-linearities and variances
Solution Approach 1:
The patent divides the ADC operating range into multiple segments and applies piecewise linear basis functions to model gain error in each segment separately. This segmentation approach captures non-linearities and variances across different operating ranges, significantly improving measurement precision while keeping each local model relatively simple
Solution Approach 2:
The patent implements a feedback mechanism where the ADC measures its own output and compares it with expected values. The error signal is fed back to the compensation logic, which adjusts the gain error compensation in real-time. This closed-loop feedback system continuously corrects measurement errors, maintaining high precision without requiring overly complex open-loop compensation circuits
2Measurement precision
If piecewise linear basis functions with least-squares analysis are employed to model and quantify gain error, then the measurement precision is improved, but the calculation complexity increases
Solution Approach 1:
The patent transforms the complex gain error compensation problem into a parameter estimation problem by using least-squares analysis. Instead of directly modeling the complex non-linear error behavior, the method changes parameters by fitting piecewise linear basis functions to measured error data, extracting coefficients that represent gain error characteristics. This parameter transformation simplifies the computational approach while maintaining high precision
Solution Approach 2:
The patent introduces piecewise linear basis functions as intermediary mathematical tools between the raw error measurements and the final gain error compensation. These basis functions serve as mediators that decompose complex error patterns into manageable linear segments, making the least-squares analysis computationally tractable while preserving measurement precision
3Measurement precision
If a DAC with known low gain error is used to generate equally spaced analog voltage levels for ADC calibration, then the measurement precision is improved, but the device complexity increases
Solution Approach 1:
The patent implements a self-service calibration approach where the system uses its own DAC to generate calibration voltage levels and its own ADC to measure them. The compensation logic then uses these self-generated measurements to determine and correct its own gain error. This self-calibration method improves measurement precision without requiring external calibration equipment, and the added complexity is minimal since it uses existing on-chip components
Data Source
AI summary
A method may include generating, via a sigma-delta DAC, a series of analog voltage levels that are equally spaced across a selected portion of ADC range; measuring, via the ADC, the series of analog voltages levels generated via the sigma-delta DAC; determining an error of a system at least partially based on a comparison of ADC output values and expected ADC output values, the system including the sigma-delta DAC and the ADC; modeling the error of the system using a combination of piecewise linear basis functions representing different types of errors or offsets; and determining a gain error of the ADC at least partially based on a coefficient of a linear basis function corresponding to the gain error of the ADC, the linear basis function one of the piecewise linear basis functions used to model the error of the system.