Prediction of the Nonlinearity by Segmentation and Matching Precision of a Hybrid R-I Digital-to-Analog Converter

The data converters’ nonlinearity, which is mainly caused by random mismatch, reflects the performance deviation between the actual realization and an ideal situation. The interpretation of the numerical relationship between the nonlinearity and matching precision for a hybrid digital-to-analog converter (DAC) consisting of a k-bit resistor-string and an m-bit current-steering array (R-I DAC) is a challenging task. In this article, we propose a method to predict the nonlinearity by the segmentation and matching-precision of an R-I DAC. First, we propose a mathematical model that focuses on the output and mismatches of an R-I DAC. The model shows that nonlinearity gets worse when the segmentation ratio (k/m) increases. Second, we derive theoretical expressions for the static nonlinearity and matching precision. It is shown that the resolution number of resistor (k) has more influence on nonlinearity than the resolution number of current steering (m). Designers can quickly determine the segmentation strategy and matching precision from the derived equations. Finally, we achieve a nonlinearity that is smaller than half the least significant bit (LSB) when the matching resolution in the bits of the resistors and current sources are k + 4 and m + 2k + 2, respectively. For the verification of the study proposed, three test groups of prototypes with different matching precisions are fabricated and measured. The measured static and dynamic performance of the designed DACs support our proposal expressions