Abstract
SIGMA-DELTA MODULATION HAS DEMONSTRATED TO BE VERY SUITED FOR the implementation of Analog-to-Digital (A/D) interfaces in many different electronic systems, covering a large number of applications from instrumentation to telecom [Nors97a][Mede99][Geer02][Schr05b][Ortm06]. This type of A/D converters (ADCs), composed of a low-resolution quantizer embedded in a negative feedback loop, uses oversampling (a sampling frequency much larger than the Nyquist frequency) to reduce the quantization error and åD modulation to push this noise out of the signal band [Inos62].
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Notes
- 1.
A large steepness in the transition band is demanded usually for the filter in order to avoid degrading the signal band. However, this specification is imposed on a digital filter and is a priori easier to fulfill than for the analog AAF of a Nyquist ADC.
- 2.
Note that a two-level quantizer has no inherent gain and, therefore, there is no obvious value for g q . The linear model used henceforth for comparators assumes that g q is such that the product of the loop gain factors is forced to unity by the feedback loop [Will91]. This model for comparators in a åDM is empirical, but its results usually compare well to computer simulations using the true non-linear quantizer function.
- 3.
A åDM is considered stable if, for bounded inputs and whatever integrators initial conditions, the internal state variables (integrator outputs) remain also bounded over time.
- 4.
Instability appears at the modulator output as a large-amplitude low-frequency oscillation, leading to long strings of alternating +1’s and −1’s [Adam97].
- 5.
This empirical condition is commonly accepted as a rule of thumb for designing stable high-order NTFs [Adam97]. Other stability criteria also exist, but none of them can ensure the stability of an arbitrary high-order single-bit åDM [Schr93]. Computer simulation is still the most reliable method to verify stability.
- 6.
Obviously, non-idealities in the analog circuitry also affect the practical performance of single-loop åDMs. Nevertheless, their operation does not rely in the cancellation of quantization errors and their sensitivity to noise leakages is therefore much lower than for cascade åDMs.
- 7.
In [Fuji00], 4-bit quantization is used in all stages of a 2-1-1 cascade åDM. The resulting scaling factor is d 3=1/32, which leads to a 30-dB increase in DR in comparison to an ideal 4th-order 4-bit åDM.
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Morgado, A., del Río, R., de la Rosa, J.M. (2011). ΣΔ ADCs: Basic Concepts, Topologies and State of the Art. In: Nanometer CMOS Sigma-Delta Modulators for Software Defined Radio. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0037-0_2
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DOI: https://doi.org/10.1007/978-1-4614-0037-0_2
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