By Jurgen van Engelen, Rudy J. van de Plassche
Sigma delta modulation has turn into a really worthwhile and generally utilized process for top functionality Analog-to-Digital (A/D) conversion of slim band indications. by using oversampling and destructive suggestions, the quantization error of a rough quantizer are suppressed in a slender sign band within the output of the modulator. Bandpass sigma delta modulation is definitely suited to A/D conversion of slim band signs modulated on a provider, as happens in communique structures equivalent to AM/FM receivers and cell phones.
a result of nonlinearity of the quantizer within the suggestions loop, a sigma delta modulator may well convey enter sign based balance homes. an analogous blend of the nonlinearity and the suggestions loop complicates the soundness research. In Bandpass Sigma DeltaModulators, the describing functionality technique is used to investigate the steadiness of the sigma delta modulator. The linear achieve version favourite for the quantizer fails to foretell small sign balance homes and idle styles effectively.
In Bandpass Sigma Delta Modulators a stronger version for the quantizer is brought, extending the linear achieve version with a section shift. research exhibits that the section shift of a sampled quantizer is in truth a section uncertainty. balance research of sigma delta modulators utilizing the prolonged version permits exact prediction of idle styles and calculation of small-signal balance barriers 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 clear out constitution must have enough levels of freedom to enforce the specified (small-signal sturdy) sigma delta modulator habit.
Bandpass Sigma Delta Modulators might be of curiosity to working towards engineers and researchers within the components of mixed-signal and analog built-in circuit design.
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Additional resources for Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects
5: Multi stage noise shaper (MASH). a second modulator. The output 01 of this modulator thus contains a quantized estimate of the quantization error signal eql. The output of the second modulator is filtered and combined with the output of the first SDM to eliminate the quantization errors of the first modulator. The output of the first modulator equals 01 (z) = 1 Z~~~z) ·l(z) + 1 + ~I (z) . 16) and the output of the second SDM can be written as 02(Z) G1(Z) 1 = 1 + G2(Z) . Eql (z) + 1 + G1(Z) .
In the case that the input signal is a sine wave Ai sin(21tj;t), the bandwidth of the distortion signals fH,/! 6 shows a typical spectrum of a first order lowpass modulator with a low frequency sine wave input. Apart from the input signal near DC, the spectrum contains frequency modulated distortion components with bandwidths that are a multiple of fD. o E -20 3fDi ............................................................... , .. 00-40 ::s. 6: Spectrum of a first order lowpass modulator with sine wave input (simulation, 2K bins).
Because each low order stage operates independently, adding additional stages does not cause stability problems. 3 Other Architectures Most realizations of oversampled noise shapers have one of the aforementioned structures. However, alternative, more exotic structures have been proposed to avoid stability problems or, for example, reduce the oversampling ratio. Some of these structures will be discussed briefly. Noise Shaping Concepts 26 A. Parallel Sigma Delta Modulators As was shown in sec. 2, a noise shaper or sigma delta modulator suppresses the quantization errors only in a part of the frequency spectrum.
Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects by Jurgen van Engelen, Rudy J. van de Plassche