Correlation of Transfer Function Implementation on Delta-Sigma Modulator Stability Analysis

Yikui ZHANG  Etsuro HAYAHARA  Satoshi HIRANO  Naohito SAKAKIBARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.4   pp.733-739
Publication Date: 2000/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Analog Signal Processing
delta-sigma modulator,  A/D converter,  auto-correlation function,  

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Higher order delta-sigma (ΔΣ) modulator with one bit quantizer is known as one of the easiest method to gain a high resolution A/D converter without the need of accurately matched components. However, stability of higher order ΔΣ modulator is still a problem during the design and implementation process. Stabilizing higher order modulator requires the proper choice of integrator gains. In this paper, a new approach on ΔΣ modulator stability analysis which based on the system auto-correlation function is proposed, and equation of NTF power integration is derived out. The specification of equation related to input signal amplitude and output quantization level is discussed. Combining with system control theory, the stability of higher order modulator (2nd and 3rd order) is evaluated. Matlab simulation confirm the proposed method. It offers an evaluation method for the choice of the in-loop integrator gains which ensure the modulator operates under the stable status, and is able to be used for designing stable higher order ΔΣ analog-to-digital converters.