Multi-Term Cosine-Sum Windows-Assisted DFT-IDFT-Based Minimum-Segment Calibration for SAR ADCs

This paper presents a DFT-IDFT-based minimum-segment calibration technique for SAR ADCs, specifically targeting capacitor mismatch-induced nonlinearity under incoherent sampling conditions. By employing multi-term cosine-sum window functions, spectral leakage is significantly suppressed, enabling accurate digital estimation of nonlinear bit-weight errors. The proposed method employs lookup tables (LUTs) to integrate DFT/IDFT and windows, greatly simplifying ADC error extraction, while employing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LDL</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}^{\mathbf {T}}$</tex-math> </inline-formula> decomposition for numerically stable least-squares estimation. A novel metric, Maximum Single-Tone Offset Attenuation (MSTOA), is introduced to evaluate window functions’ efficacy in suppressing spectral leakage. Among digital calibration methods, the minimum-segment approach achieves substantial improvement in calibration accuracy while maintaining comparable computational complexity. The non-iterative, one-shot error extraction method eliminates convergence delays inherent in iteration-based methods. Additionally, built-in self-test (BIST) capability enables concurrent dynamic performance evaluation. Measurement results from a 20-bit 1-MS/s prototype implemented in 180-nm CMOS demonstrate that post-calibration SNDR/SFDR can be improved by 22.7dB and 27.3 dB, respectively.