Correlation of transfer function implementation on delta-sigma modulator stability analysis

Higher order delta-sigma (Delta Sigma) 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 hi gher order Delta Sigma modulator is still a problem during the design and i mplementation process. Stabilizing higher order modulator requires the prop er choice of integrator gains. In this paper, a new approach on Delta Sigma modulator stability analysis which based on the system auto-correlation fu nction is proposed, and equation of NTF power integration is derived out. T he specification of equation related to input signal amplitude and output q uantization level is discussed. Combining with system control theory, the s tability 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 oper ates under the stable status, and is able to be used for designing stable h igher order Delta Sigma analog-to-digital converters.