This paper proposes a Multi-stAge noise SHaping (MASH) digital delta-sigma modulator (DDSM) with negative feedback to acquire the maximum sequence length. The mathematical analysis shows that the sequence length is [Formula: see text], which is not affected by the input values and initial conditions, where [Formula: see text] is the smallest prime number above the quantization interval [Formula: see text], and [Formula: see text] is the order of the MASH DDSM. Moreover, the influence of the negative feedback on the input range is analyzed. Finally, the simulations and experiments are performed to verify the theoretical analysis.
This paper presents a new multi-stage noise-shaping (MASH) digital delta-sigma modulator (DDSM), denoted as HJ-MASH DDSM which can remove spurs in the output spectrum and has long sequence lengths than Jinook structure and HK-MASH in the worst input case by applying HK-EFM in the first stage error feedback modulator (EFM) of the DDSM. In addition, the proposed HJ-MASH DDSM lowers the difficulty of constructing higher order MASH DDSMs compared to HK-MASH DDSM. While the performance and stability are all superior to Jinook structure for all constant inputs, especially for the input which correspond to minimum cycle lengths. The digital delta-sigma modulator applied in fractional-N frequency synthesizers ameliorates the synthesizer's spectral purity apparently by verification.
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