Calibration of residual errors using least-mean-squares (lms) and stochastic-gradient methods for an analog-to-digital converter (adc) with a pre-calibrated lookup table

Abstract

A first calibration measures capacitor array mis-match and updates a Look-Up Table (LUT) with calibrated weights that are copied to both a positive LUT and a negative LUT, and then adjusted for non-linearity errors by a second calibration using a Least Mean-Square (LMS) method. The binary code in the Successive-Approximation Register (SAR) is complemented to generate a complement code with a sign bit. When the sign bit is positive, entries for complement code bits=1 are read from the positive LUT and summed, a first offset added, and the sum normalized to get a corrected code. When the sign bit is negative, entries for complement code bits=0 are read from the negative LUT and summed, a second offset added, and the sum normalized to get the corrected code. A Multi-Variable Stochastic Gradient Descent method generates polynomial coefficients that further correct the corrected code.