Excess loop delay in continuous-time delta-sigma modulators

Continuous-time (CT) delta-sigma modulators (ΔΣM´s) suffer from a problem not seen in discrete-time (DT) designs, that of excess loop delay: nonzero delay between the quantizer clock edge and the time when a change in output bit is seen at the feedback point in the modulator. This paper analytically shows how such delay affects the equivalence between the CT modulator loop filter and its DT counterpart. The effect of this delay on modulator dynamic range is studied through simulation for the standard double-integration (low pass) CT modulator and its equivalent fourth-order f_s/4 band pass circuit. For the first time, the results are extended to higher order low-pass and bandpass designs, as well as multibit designs. Methods for alleviating the performance loss caused by excess loop delay are also discussed