LMS-Based Noise Leakage Calibration of Cascaded Continuous-Time $\Delta \Sigma$ Modulators

In cascaded ΔΣ modulators (DSMs), the quantization noise of the earlier stage leaks to the output unless completely cancelled by the digital noise cancellation filter (NCF). The noise leakage is worse in the continuous-time (CT) implementation due to the poorly controlled time constant of the analog loop filter. A parameter-based continuous-time to discrete-time transform is developed to get an exact digital NCF, and the analog filter time constant is calibrated to match with the digital NCF. A binary pulse tone is injected into the quantizer to detect the filter time-constant error, and eliminated by zero-forcing its residual power based on the adaptive least-mean-square (LMS) algorithm. A 2-1-1 cascaded CT-DSM prototype in 0.18-μm CMOS demonstrates that the spectral density of the leaked noise is lower than 10 nV/??Hz after the capacitors in the Gm-C loop filters are trimmed with 1.1% step. With a 1-V_pp full-scale input, it achieves a dynamic range of 68 dB within 18-MHz bandwidth at an over-sampling ratio of 10. The analog core and the digital logic occupy 1.27 mm²,and consume 230 mW at 1.8 V.