By Friedel Gerfers, Maurits Ortmanns
Sigma-delta A/D converters are a key development block in instant and multimedia purposes. This complete e-book bargains with all correct features coming up in the course of the research, layout and simulation of the now common continuous-time implementations of sigma-delta modulators. the result of numerous years of study via the authors within the box of CT sigma-delta modulators are coated, together with the research and modeling of other CT modulator architectures, CT/DT loop filter out synthesis, a close mistakes research of all elements, and attainable compensation/correction schemes for the non-ideal habit in CT sigma-delta modulators. tips for acquiring low-power intake and a number of other functional implementations also are provided. it really is proven that every one the proposed new theories, architectures and attainable correction suggestions were proven by way of measurements on discrete or built-in circuits. Quantitative effects also are supplied, therefore allowing prediction of the ensuing accuracy.
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Extra info for Continuous-Time Sigma-Delta A/D Conversion: Fundamentals, Performance Limits and Robust Implementations
Typical spectrum with signal peak and harmonics – In-band noise. The integrated in-band noise (IBN) is a common converter measure, because it gives the total output noise in the band of interest and thus the minimum resolvable signal power. In spite of its little importance as a real ADC performance metric in terms of number of bits, it gives direct insight into the inﬂuence of architectural alternatives, nonideal behavior and so on. Therefore, it will be most often used throughout this work. Additionally it should be noted that the IBN contains all in-band power including noise, distortion or other tones.
But while the implementation of the internal ADC is rather simple, because any errors are subject to the maximum noise shaping , the feedback DAC requires a linearity better than the overall modulator . This is due to the DAC errors, which are directly fed into the input of the modulator as can be seen from Fig. 9. 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.
4 Σ∆ Modulator Loop Filter Stability and Scaling The above presented architectures provide the possibility to implement a noise-transfer and signal-transfer function with a certain ﬁlter characteristic. 30 2 Basic Understanding of Σ∆ A/D Conversion But together with considering about the loop ﬁlter implementation, the ﬁnding of such loop ﬁlter is of major interest. The well-known drawback of single-loop single-bit Σ∆ modulators with orders higher than two is their tendency to instability . Thereby, stability is deﬁned as a modulator condition, where all internal state variables, which are the integrator outputs, remain bounded over time .
Continuous-Time Sigma-Delta A/D Conversion: Fundamentals, Performance Limits and Robust Implementations by Friedel Gerfers, Maurits Ortmanns