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DC Analysis of High Order Sigma Delta Modulators

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A new method for the DC analysis of a Sigma Delta modulator (SDM) is presented. The model used for the description of a SDM is adopted from Candy's model for a first order SDM. However, where Candy's model is exact for a first order SDM, it fails to be so in a higher order case. In our model, we deal with this by the introduction of stochastic behaviour of the SDM, and obtain the probability density distribution function of some variables which determine many of the characteristics of the SDM in the time domain. Comparison with simulation results shows that the assumption of stochastic behaviour is rather good for SDM orders greater than 3, which display significant noise shaping. For lower orders (or less aggressive noise shaping) the approximation is less good. As an aside, the new model of sigma delta modulation also clarifies why the 'time-quantized' dither approach presented by Hawksford is much better compared to standard quantizer dithering.

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