By Friedel Gerfers, Maurits Ortmanns
Sigma-delta A/D converters are a key construction block in instant and multimedia purposes. This complete publication bargains with all appropriate points coming up throughout the research, layout and simulation of the now frequent continuous-time implementations of sigma-delta modulators. the result of numerous years of analysis by means of 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, an in depth mistakes research of all parts, and attainable compensation/correction schemes for the non-ideal habit in CT sigma-delta modulators. information for acquiring low-power intake and a number of other functional implementations also are provided. it truly is proven that each one the proposed new theories, architectures and attainable correction innovations were proven by way of measurements on discrete or built-in circuits. Quantitative effects also are supplied, hence permitting prediction of the ensuing accuracy.
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Additional info for Continuous-Time Sigma-Delta A/D Conversion: Fundamentals, Performance Limits and Robust Implementations
5 Oversampled Noise-Shaping Converters: Σ∆ ADC ua (t) u(t) fS /2 Antialiasing filter u(n) xd (n) S/H H(z) q(n) yd (n) y(n) - DAC 19 fB Digital filter SD modulator Down sampling Decimator Fig. 9. Block diagram of a Σ∆ ADC NTFOpt = STFOpt = 0, 1, −fB ≤ f ≤ fB else . 10) This corresponds to an ideal low-pass ﬁlter for the STF and to an ideal high-pass ﬁlter for the NTF, both with a cut-oﬀ frequency of at least the signal bandwidth fB . Thus, the quantization noise is shaped away from the desired frequency range, leading to a noise-shaping converter.
The above mentioned digital low-pass ﬁlter 18 2 Basic Understanding of Σ∆ A/D Conversion X(f ) HLP (f ) -fS Se (f ) = IBN - fB fB f fS (a) X(f ) HLP (f ) IBNOSR Se (f ) -fS - fS /2 - fB fB fS /2 fS f (b) Fig. 8. Illustration of spectral eﬀect of oversampling. (a) Quantization noise and in-band noise for OSR = 1; (b) quantization noise and in-band noise for OSR = 4 is usually called the decimation ﬁlter or simply the decimator. Beyond the elimination of high frequency noise components its task is also to reduce the sample rate at the overall output to the Nyquist rate.
In this work, the Blackman window has been used. To prevent signal power mismatch, after the calculation of the periodogram the eﬀect of windowing has been reversed as proposed in  and shown in Appendix A. Nevertheless, the eﬀect of leakage and even uncertainty remain in this analysis, and slight variations in the calculation method can result in more than a trivial diﬀerence. Thus one should not expect the decimal places of the calculation results or simulations to be meaningful , even if they are often given in the literature.