By Jurgen van Engelen, Rudy J. van de Plassche
Sigma delta modulation has develop into a really worthwhile and greatly utilized strategy for prime functionality Analog-to-Digital (A/D) conversion of slim band indications. by utilizing oversampling and adverse suggestions, the quantization error of a rough quantizer are suppressed in a slim sign band within the output of the modulator. Bandpass sigma delta modulation is easily fitted to A/D conversion of slender band indications modulated on a provider, as happens in verbal exchange platforms corresponding to AM/FM receivers and cell phones.
because of the nonlinearity of the quantizer within the suggestions loop, a sigma delta modulator may well show enter sign established balance houses. an identical 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 higher version for the quantizer is brought, extending the linear achieve version with a part shift. research indicates that the section shift of a sampled quantizer is actually 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 soundness homes have a substantial influence at the layout of single-loop, one-bit, high-order continuous-time bandpass sigma delta modulators. The continuous-time bandpass loop clear out constitution must have enough levels of freedom to enforce the specified (small-signal solid) sigma delta modulator habit.
Bandpass Sigma Delta Modulators might be of curiosity to practising engineers and researchers within the components of mixed-signal and analog built-in circuit design.
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Extra info for Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects
In Fig. 10 the relationship between the maximum deviation fD2 (see Fig. 9) of the distortion components, and the input amplitude Ai and the input frequency /; is shown. The bandwidth of the modulated tones around fs/4 indeed depends proportionally to the input amplitude and inverse proportionally to the input frequency. The frequency modulated distortion components or tones located around fs/4 at low input amplitudes have a noticeable effect on the SNR of the modulator. When the input frequency and amplitude are such that the bandwidth of these distortion components is small, they will be located near fs /4.
A more elaborate model for calculating the quantization noise was developed by ARDALAN and PAULOS. In  they suggested to use a separate gain for the signal and the quantization noise. By doing so, the correlation between the input of the quantizer x and the quantization noise nq is incorporated in the model. In the model of Fig. 2 the input of the quantizer and the quantization errors are assumed to be uncorrelated. 5). Instead, the two parameters are solved by minimizing the rms error in modeling the nonlinear quantizer.
O E -20 3fDi ............................................................... , .. 00-40 ::s. 6: Spectrum of a first order lowpass modulator with sine wave input (simulation, 2K bins). The low frequency distortion components fHe,1I in the output of the modulator cause a deviation in the SNR vs. input power characteristic of the first order SDM. Caused by the amplitude distribution of a sine wave, most of the distortion power will be located near the frequencies n· fD. For large input amplitudes, these distortion components will not fall inside the signal bandwidth [0, fb) in which the SNR is measured.
Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects by Jurgen van Engelen, Rudy J. van de Plassche
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