Discrete-time simulation of arbitrary digital/analog converter waveforms in continuous-time sigma-delta modulators

In this paper, the inclusion of arbitrary feedback pulses into the method of discrete-time simulation of continuous-time sigma-delta modulator is investigated. Although rectangular feedback pulses cover the majority of the published sigma-delta modulator circuits, there arise well known advantages from other waveform shapes, such as reduced sensitivity to excess-loop-delay in the feedback path, finite gain bandwidths in the operational amplifiers and clock-jitter. In order to also utilize the benefit of fast discrete-time simulations of continuous-time modulators in the case of non-rectangular digital-to-analog converter waveforms, this work provides the mathematical background for accurate modeling. Comparative simulations show a speed advantage of up to more than three order of magnitude.