Stability and Performance Analysis of an Adaptive Sigma–Delta Modulator

This work develops an adaptive sigma–delta modulator that is based on adapting the quantizer step-size using estimates of the quantizer input rather than the modulator input. The adaptive modulator with a first-order noise shaping filter is shown to be bounded-input bounded-output stable. Moreover, an analytical expression for the signal-to-noise ratio is derived, and it is shown to be independent of the input signal strength. Simulation results confirm the signal-to-noise ratio performance and indicate considerable improvement in the dynamic range of the modulator compared to earlier structures.