By Dr.-Ing. Maurits Ortmanns, Dr. Friedel Gerfers (auth.)
Sigma-delta A/D converters are a key construction block in instant and multimedia functions. This complete booklet bargains with all proper features coming up throughout the research, layout and simulation of the now common continuous-time implementations of sigma-delta modulators. the result of numerous years of study by way of the authors within the box of CT sigma-delta modulators are coated, together with the research and modeling of alternative CT modulator architectures, CT/DT loop clear out synthesis, a close errors research of all elements, and attainable compensation/correction schemes for the non-ideal habit in CT sigma-delta modulators. assistance for acquiring low-power intake and a number of other functional implementations also are awarded. it truly is proven that every one the proposed new theories, architectures and attainable correction ideas were proven through measurements on discrete or built-in circuits. Quantitative effects also are supplied, therefore allowing prediction of the ensuing accuracy.
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Additional resources for Continuous-Time Sigma-Delta A/D Conversion: Fundamentals, Performance Limits and Robust Implementations
Here, the intrinsic resolution is increased proportionally to (2Bint − 1)2 , because with increasing quantizer resolution in accordance to Fig. 4) the quantizer step width and therewith the quantization noise power proportionally decrease. Furthermore, the incorporation of multibit internal quantization tends to make higher order modulators more stable, the internal quantizer gain can be approximated to be unity, and the requirement for loop gain scaling is reduced. Thus almost ideal performance is obtained for medium modulator orders .
The determination of kq0 together with the critical gain kq,crit then yields an estimate, if the modulator is conditionally or unconditionally stable or even completely unstable. , for zero input signal all poles are inside the unit circle, but for increasing input amplitude at least one pole shifts into instability The given root-locus method is a linear approach to a strongly nonlinear system. Thus, this conditional stability and the ﬁnding of optimal scaling coeﬃcients must be conﬁrmed by behavioral simulations, and is usually based on two requirements : ﬁrst, the modulator input signal has to be bounded into a speciﬁc interval, and second, the scaling has to prevent the noise-transfer function from peaking at high frequencies.
In [47, 87] the quantizer in ﬁrst-order and second-order modulators has been modeled using the loop ﬁlter unity gain approximation. This is to assume a quantizer gain kq , such that the product of the loop ﬁlter gains and the quantizer gain around the outermost feedback loop of a Σ∆ modulator as in Fig. 14 is equal to 1. It should be noted that the only justiﬁcation for this approximation is the good agreement of analytical and simulation results, which were stated in [47, 87]. But it is to mention that in both works, only ﬁrst-order and second-order loops were considered.