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Additional info for Continuous-Time Sigma-Delta A D Conversion: Fundamentals, Performance Limits and Robust Implementations (Advanced Microelectronics, Volume 21)
In general, the overall performance of a Σ∆ modulator is characterized by the dynamic metrics, which can be subdivided into spectral, frequency domain, and power metrics. 1 Frequency Domain Metrics The analysis of the power or amplitude spectral density of the ADC output signal is straightforward, because the proper functionality can be almost directly seen. Especially in the case of the Σ∆ modulator, which is a noiseshaping converter, the analysis of the frequency domain representation of the time domain output bits is of interest.
16. Implementation of a N th order single-bit Σ∆ modulator consisting of a chain of integrators with weighted feed-forward ai summation Nonetheless, as was the case for the pure feedback architecture, for a desired noise-shaping function, the STF is also chosen. In addition, the STF of the feed-forward architecture in Fig. 16 contains peaking at high frequencies due to the resulting ﬁlter characteristic; with input signals at these frequencies a modulator with feedforward summation could overload, thus precautions have to be taken .
7 Single-Loop, Single-Bit, Higher Order Σ∆ Modulators 25 a low resolution, the linearity of the DAC has to be as good as the accuracy of the overall modulator. For a single-bit internal quantizer this problem does not arise, because a two level DAC is intrinsically linear. Here, only oﬀset and gain errors remain, which a Σ∆ modualtor is highly tolerant to . Actually, there have been many publications dealing with techniques to achieve the linearity requirements, based on design consideration  as well as digital or analog correction techniques [4, 8, 68–70].