Multi-Stage Noise-Shaping Continuous-Time Sigma-Delta Modulator

The design of a single-loop continuous-time ∑∆ modulator (CT∑∆M) with high resolution, wide bandwidth, and low power consumption is very challenging. The multi-stage noise-shaping (MASH) CT∑∆M architecture is identified as an advancement to the single-loop CT∑∆M architecture in order to satisfy the ever stringent requirements of next generation wireless systems. However, it suffers from the problems of quantization noise leakage and non-ideal interstage interfacing which hinder its widespread adoption. To solve these issues, this dissertation proposes a MASH CT∑∆M with on-chip RC time constant calibration circuits, multiple feedforward interstage paths, and a fully integrated noise cancellation filter (NCF). The prototype core modulator architecture is a cascade of two single-loop second- order CT∑∆M stages, each of which consists of an integrator-based active-RC loop filter, current-steering feedback digital-to-analog converters, and a four-bit flash quantizer. On-chip RC time constant calibration circuits and high gain multi-stage operational amplifiers are realized to mitigate quantization noise leakage due to process variation. Multiple feedforward interstage paths are introduced to (i) synthesize a fourth-order noise transfer function with DC zeros, (ii) simplify the design of NCF, and (iii) reduce signal swings at the second-stage integrator outputs. Fully integrated in 40 nm CMOS, the prototype chip achieves 74.4 dB of signal-to-noise and distortion ratio (SNDR), 75.8 dB of signal-to-noise ratio, and 76.8 dB of dynamic range in 50.3 MHz of bandwidth (BW) at 1 GHz of sampling frequency with 43.0 mW of power consumption (P). It does not require external software calibration and possesses minimal out-of-band signal transfer function peaking. The figure-of-merit (FOM), defined as FOM = SNDR + 10 log10(BW/P), is 165.1 dB