# High-Order Sigma-Delta Modulators

## Abstract

This chapter comprises two sets of exercises. In the first set, the main properties of a third-order modulator (MOD3) are investigated, following the procedure of previous chapters. Based on the simulations proposed, it is demonstrated that modulators with noise-shaping order higher than two can be unstable for some or even all possible inputs, usually displaying chaotic limit cycle behavior unrelated to the input signal when unstable. However, careful architecture selection for single-loop modulators – which entails controlling the form of NTF to limit its maximum gain – and the implementation of multi-bit quantization will be investigated, with the aim to demonstrate how high-order modulators stability and stable input range can be increased. Following the results obtained from the simulations proposed, an investigation of the theory required to design efficient high-order modulators will be presented. The architectures analyzed comprise Cascaded Integrators Feedback (CIFB), Cascaded Integrators Feedforward (CIFF), Cascaded Resonators Feedback (CRFB), and Cascaded Resonators Feedforward (CRFF). Regarding the second section of this chapter, the widely used MATLAB®-based Schreier’s Delta-Sigma Toolbox is introduced as an effective tool to generate coefficients for generic high-order modulator structures. Moreover, a simple design example to demonstrate the procedure to generate the coefficients required by the Simulink® models provided will be presented.

## Supplementary material

## References

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