Analytical method to determine optimal out-of-band gain in multi-bit delta-sigma modulator

Abstract

A simple, systematic and deterministic MATLAB simulation which employs Risbo method and analytical simulation is proposed to determine the optimal out-of-band gain to achieve a maximal SNR and the maximum stable amplitude in a multi-bit delta-sigma modulator. Using the proposed method, a 128MS/s, 2MHz signal bandwidth 4^th order 2-bit continuous-time delta-sigma modulator is designed and implemented in 0.18µm CMOS technology to verify the concept. As a result, the modulator achieves a peak SNDR of 79.3dB and a dynamic range of 83dB for a 2MHz signal bandwidth (OSR = 32) while consuming only 7.8mW from 1.8V supply.