Analysis and design of one-bit noise-shaping quantizer using variable structure control approach

This paper offers a straightforward analysis of a one-bit noise-shaping quantizer based on variable structure control methods. The method uses the concept of equivalent control to access the bound on the state signals when the sliding condition is reached. For a stable loop filter, the global stability can be proved to exist by using the Lyanpunov stability theory. For an unstable loop filter, this paper proposes a state constraint approach to ensure that the sliding condition is achieved. Simulation examples and an experimental circuit constructed using off-the-shelf electronic components are given to demonstrate the correctness of the theoretical analysis.