Stability and sensitivity analysis and optimization of delta sigma modulators

Delta sigma modulation is a popular form of analog-to-digital and digital-to-analog conversion, but suffers from stability problems for many designs and many input signals. In this paper, we present a systematic method to design and optimize the high order and multibit ΔΣ modulators based on their stability analysis. Also, the sensitivity of modulator performance to variation of different realization coefficients is analyzed and different case studies are presented. The main advancement of the presented design process lied on maximizing modulator dynamic range considering practically stability and sensitivity margins which were not clearly analyzed in previously reported similar works. By this mean, modulator peak SNR can gain some further improvement in the order of 10dB in certain multibit applications. The results of this paper would enable the optimization and design of high order multibit ΔΣ modulators based on the stability region of ΔΣ modulator.