Hybrid modeling techniques for low OSR cascade continuous-time ΣΔ modulators

Approaches for modeling continuous-time (CT) SigmaDelta modulators based on the Bilinear (BT), Lossless-Discrete Integration (LDI) and Impulse Invariant (II) transformations are compared for low-OSR cascade architectures. A hybrid modeling approach is introduced that combines the BT and LDI transformations, and enables direct synthesis of the CT modulator from a discrete-time (DT) template. The resulting CT architecture is identical to the DT counterpart; i.e., no new signal paths are introduced. Moreover, frequency warping is not required as in the BT case for low-OSR modulators.