Continuous-time (CT) sigma-delta (61) modulators are growing increasingly popular in wide-band analog-digital conversion. High orders of quantization noise shaping, and multibit quantizers, are used to compensate for the low oversampling ratios in wide-band applications. These, however, add circuit complexities and excess loop delay that are detrimental to the 61 control loop. This paper presents an exact mathematical analysis technique, based on the CT-discrete time equivalence, that can take these effects into account. A design-by-optimization approach based on that analysis is used to compensate for these effects, avoid intractability issues and to gain flexibility in the design. It is also shown that it is advantageous not to fix the position of the quantization noise-shaping zeros in the signal band.Index Terms-Continuous-time (CT) sigma-delta (61), CT-discrete-time (DT) equivalence, design by optimization, impulse invariance.

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