A method for the discrete-time simulation of continuous-time Sigma-Delta modulators

This paper presents a method for the discrete-time (DT) simulation of continuous-time (CT) Sigma-Delta modulators. Via the application of Lifting, correction values for each state variable of a modulator are calculated, which subsequently are used to calibrate online these state variables during a DT simulation of the CT system. At the sampling instants, the values of the DT state variables are thus exactly equalized to those of the given CT modulator while the time consuming CT simulation itself has been replaced by an efficient and rapid DT one. A simple second order modulator serves as an example to illustrate the application of Lifting not only to an ideal but also to a non-ideal modulator covering typical non-idealities such as finite opamp gain, finite gain-bandwidth, excess loop delay and even jitter(1).