The Error Analysis of Bit Weight Self-Calibration Methods for High-Resolution SAR ADCs

High-resolution successive approximation register (SAR) analog-to-digital converters (ADCs) commonly need to calibrate their bit weights. Due to the nonidealities of the calibration circuits, the calibrated bit weights carry errors. This error could propagate during the calibration procedure. Due to the high precision requirement of these ADCs, such residue error commonly becomes the signal-to-noise-and-distortion ratio (SNDR) bottleneck of the overall ADC. This article presents an analysis of the residue error from bit weight self-calibration methods of high-resolution SAR ADCs. The major sources contributing to this error and the error reduction methods are quantitively analyzed. A statistical analysis of the noise-induced random error is developed. Our statistical model finds that the noise-induced random error follows the chi-square distribution. In practice, this random error is commonly reduced by repetitively measuring and averaging the calibrated bit weights. Our statistical model quantifies this bit weight error and leads to a clearer understanding of the error mechanism and design trade-offs. Following our chi-square model, the SNDR degradation due to the circuit noise during the calibration can be easily estimated without going through the time-consuming traditional transistor-level design and simulation process. The required repetition time can also be calculated. The bit-weight error models derived in this article are verified with measurement on a 16-bit SAR ADC design in a 180-nm CMOS process. Results from our model match both simulations and measurements well.