Built-in self calibration for process variation in single-loop continuous-time sigma-delta modulators

A novel built-in self calibration technique for single-loop continuous-time sigma-delta modulators is proposed. Using out-of-band test signal injection and digital cancellation, this technique provides an area efficient, highly digital calibration structure to counteract gain variations in the loop filter. The calibration methodology and mathematical analysis are presented using a 2
^nd
order multibit sigma-delta modulator as a proof of concept. The effect of the finite gain-bandwidth of amplifiers is included when evaluating the calibration method. The proposed technique is validated through corner simulations using behavioral models and it shows that degradation in the signal-to-noise-plus-distortion ratio can be counteracted.