Influence of finite integrator gain bandwidth on continuous-time sigma delta modulators

This paper presents analytical considerations on the gain-bandwidth requirements in continuous-time ΣΔ modulators with rectangular and decaying feedback pulse forms. Therefore the influence of finite GBW is modelled as an integrator gain error and an additional loop delay in the feedback path, or as a slowdown of the feedback slope respectively. The presented models provide a very good insight into the influence of finite gain-bandwidth on the performance of continuous-time modulators. Additionally it could be shown, that the bandwidth can be chosen much lower as usually done in designs, and moreover, that it should be possible to reduce its influence by coefficient tuning. Both, the model and the analytical considerations are proven by simulations.