Bounding attraction areas of a third-order sigma-delta modulator

The paper introduces a novel approach, using the critical planes tool and noninvertible map theory, to analyze the boundaries of attraction areas for the integrator outputs of third-order sigma-delta modulators. This allows estimation of the clipping level of the modulators and determination of the required on-chip area for switched-capacitors in the implementation of these modulators. This approach is also very flexible and may be applied to the design and implementation of a range of sigma-delta modulator architectures.