Optimal Design for Delta–Sigma Modulators With Root Loci Inside Unit Circle

Single-stage high-order delta-sigma modulators (DSMs) designed by methods with root loci inside the unit circle (RLiUC) can operate stably with full-scale input. The previously published RLiUC method uses a conservative approach to design the loop filter´s transfer function H(z) of a DSM, thus resulting in a modest SNR. In this brief, the pole-zero locations of H(z) are optimized to maximize the stable input range while minimizing SNR reduction. Accordingly, optimal third- and fourth-order RLiUC DSMs are designed, and a systematic method for orders higher than 4 is developed. The considerations for the optimal design are the in-band noise attenuation and out-of-band gain of RLiUC DSMs. With an oversampling ratio of 32 and a quantizer bit number of 6, the optimized fourth-order RLiUC DSM achieves a peak SNR of 109 dB. Compared with the previously published result, the SNR is improved by 20 dB. To demonstrate the advantage of RLiUC DSMs, an application example for a class-D amplifier is used. With the RLiUC DSM, the achieved low-distortion output power of class-D amplifiers can be maximized.