Stability analysis of high-order delta-sigma modulation for ADC´s

A model for ΔΣ A/D modulators that allows stability analysis using linear methods is described. This model draws out the dependence of stability on system parameters such as integrator gains and delays as well as the dependence on dynamic characteristics such as input amplitude, transients, and initial conditions. In addition, high-order systems are found to be prone to a previously unrecognized source of instability, saturation limit cycles. Stabilizing high-order systems requires controlling the saturation limit cycles, minimizing the integrator delays, and the proper choice of integrator gains. The dominant means of stabilizing high-order systems, however, is identified to be the use of multi-bit quantization since this transforms the nature of the system rather than just restricting the region of operation