Theoretical total harmonic distortion evaluation based on digital to analogue converter mismatch to improve the linearity of successive approximation register analogue to digital converter

Abstract

Abstract Mismatch in the binary‐weighted capacitive digital‐to‐analog converter (DAC) greatly affects the linearity of the successive‐approximation‐register (SAR) ADC by deteriorating the total harmonic distortion (THD). In this study, a theoretical relationship between the THD and the mismatch error of DAC array in SAR ADC is derived through discrete Fourier transform (DFT) analysis of the time‐based integral error (TIE) of the ADC's output codes, which has no specific requirement on the type of the input signals. Guided by the theoretical THD expression, the trade‐off among the linearity, design complexity, power consumption and chip area can be balanced easily. The presented formula is verified by a design example of 12‐bit SAR ADC with dynamic‐element‐matching (DEM) technique, where the 3‐bit LSBs from the SAR ADC are used to generate the randomised DEM state according to the previous THD evaluation. The linearity is enhanced by 9 dB approximately with very low hardware complexity and extremely small extra power consumption of 2 μW.

Keywords

• harmonic distortion
• digital‐analogue conversion
• analogue‐digital conversion
• discrete Fourier transforms