Download Bandpass Sigma Delta Modulators: Stability Analysis, by Jurgen van Engelen, Rudy J. van de Plassche PDF

By Jurgen van Engelen, Rudy J. van de Plassche

Sigma delta modulation has develop into a really valuable and commonly utilized strategy for prime functionality Analog-to-Digital (A/D) conversion of slender band indications. by utilizing oversampling and unfavourable suggestions, the quantization mistakes of a rough quantizer are suppressed in a slim sign band within the output of the modulator. Bandpass sigma delta modulation is easily suited to A/D conversion of slim band indications modulated on a provider, as happens in verbal exchange structures corresponding to AM/FM receivers and cellphones.
a result of nonlinearity of the quantizer within the suggestions loop, a sigma delta modulator may well express enter sign established balance houses. a similar mixture of the nonlinearity and the suggestions loop complicates the soundness research. In Bandpass Sigma DeltaModulators, the describing functionality process is used to investigate the soundness of the sigma delta modulator. The linear achieve version standard for the quantizer fails to foretell small sign balance houses and idle styles correctly.
In Bandpass Sigma Delta Modulators a much better version for the quantizer is brought, extending the linear achieve version with a part shift. research exhibits that the part shift of a sampled quantizer is in reality a part uncertainty. balance research of sigma delta modulators utilizing the prolonged version permits exact prediction of idle styles and calculation of small-signal balance limitations for loop filter out parameters. A simplified rule of thumb is derived and utilized to bandpass sigma delta modulators.
the steadiness homes have a substantial impression at the layout of single-loop, one-bit, high-order continuous-time bandpass sigma delta modulators. The continuous-time bandpass loop filter out constitution must have adequate levels of freedom to enforce the specified (small-signal solid) sigma delta modulator habit.
Bandpass Sigma Delta Modulators may be of curiosity to training engineers and researchers within the components of mixed-signal and analog built-in circuit design.

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Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects

Sigma delta modulation has develop into a really invaluable and extensively utilized approach for top functionality Analog-to-Digital (A/D) conversion of slender band indications. by utilizing oversampling and unfavorable suggestions, the quantization mistakes of a rough quantizer are suppressed in a slim sign band within the output of the modulator.

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Additional info for Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects

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L3. 13: Interpolative loop filter topology. Although for practical reasons these topologies can be used for the implementation of the loop filter, they are a special case and can be transformed into the direct form shown in Fig. 14 [9]. The transfer function of this discrete time filter equals G{z) = Gc{z) Gd{Z) = co + C\z-I + C2Z- 2 + ... + CNZ- N 1- dlz- I - d2C 2 _ ... 26) in which N is the order of the loop filter, Cn (n = 0, 1, ... ,N) are the feedforward coefficients determining the zeroes of G{z) and dn (n = 1,2, ...

For other frequencies, the quantization errors are amplified (see Fig. 3). In order to increase bandwidth in which the quantization errors will be sufficiently attenuated, several architectures have been proposed placing multiple noise shapers or sigma delta modulators in parallel. An intuitive approach is to divide the required bandwidth into several smaller frequency ranges (or channels) and use a separate SDM for each channel [20]. 6 shows a block-diagram of such a multi-band parallel SDM. The input is separated into K chan- in ~I~ ~I~ .

When the quantizer error signal eq and the dither signal d are assumed to be uncorrelated, a linear prediction model similar to Fig. 2 can be used to predict the in-band noise in the output of the quantizer. 2 Chaotic Modulators Another method to reduce the pattern noise and tones in the output of a modulator is to design the loop filter such that the SDM exhibits chaotic behavior [39]. In the context of dynamical systems, chaotic behavior or chaos is defined as follows [40]: The behavior of a system is called chaotic when a very small perturbation in the initial state of the system results in asymptotically diverging but bounded state space trajectories of the system.

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