Optimal Design of Multibit Interpolative Sigma Delta Modulators Subject to Absolute Stability Criterion

Abstract

In this paper, an optimal design of a multibit interpolative sigma delta modulator (SDM) based on the absolute stability criterion is proposed. There are two types of midtread quantizers, namely, the uniform midtread quantizer and the nonuniform midtread quantizer. It is shown in this paper that the uniform midtread quantizer is the optimal one between these two types of the midtread quantizers in the sense of minimizing the maximum output input ratio of the midtread quantizer. A loop filter of the multibit interpolative SDM is designed based on the minimization of the energy of the noise transfer function in signal band subject to the strictly stable or the marginally stable condition of the loop filter, the absolute stability criterion, and the specifications on both the noise transfer function in the signal band and the magnitude response of the loop filter outside the signal band. Computer numerical simulation results show that our proposed multibit interpolative SDM achieves a broader stability margin and a higher signal-to-noise ratio compared to the state-of-art designs.