Digital extraction of quantization error and its applications to successful design of sigma-delta modulator

A new technique to evaluate the quantization error of cascaded sigma-delta modulators in digital domain is presented. It avoids the complications associated with analog extraction of the quantization error in multistage noise shaping (MASH) modulators before feeding the error to the proceeding stage. Instead, the quantization error is estimated and cancelled out by adding a digital subtractor and by injecting a purely analog signal from the preceding stage to the next stage. In comparison to conventional MASH modulator structure, analog circuit requirements of the modulator are therefore relaxed, and the number of switched-capacitor digital-to-analog converters and the associated switching energy are lowered. In the absence of extra switching blocks, less flicker and thermal noise would be also injected into the circuit. Different implementations of MASH modulator are presented and analyzed based on the proposed digital quantization error extraction technique. Behavioral-level simulation results prove the mathematical equivalence of the proposed structures with successful MASH designs found in the literature, and confirm the effectiveness of the idea. For a - 1.4 dB, 19.8 kHz input and an oversampling ratio of 16, a modified 1-V 20-MS/s 2 + 2 MASH modulator achieves a signal-to-noise-and-distortion ratio (SNDR) of 78 dB, when the input of the first quantizer is fed to the second stage. The second design based on digital extraction of quantization error achieves a 71 dB SNDR for a - 8.0 dB, 19.8 kHz input, when the second stage is fed by the output of the first integrator.