By Jurgen van Engelen, Rudy J. van de Plassche
Sigma delta modulation has develop into a truly invaluable and broadly utilized method for prime functionality Analog-to-Digital (A/D) conversion of slim band signs. by utilizing oversampling and unfavorable suggestions, the quantization blunders of a rough quantizer are suppressed in a slim sign band within the output of the modulator. Bandpass sigma delta modulation is definitely fitted to A/D conversion of slim band indications modulated on a provider, as happens in communique structures corresponding to AM/FM receivers and cellphones.
as a result of the nonlinearity of the quantizer within the suggestions loop, a sigma delta modulator might express enter sign based balance homes. an identical mixture of the nonlinearity and the suggestions loop complicates the steadiness research. In Bandpass Sigma DeltaModulators, the describing functionality approach is used to research the soundness of the sigma delta modulator. The linear achieve version usual for the quantizer fails to foretell small sign balance homes and idle styles thoroughly.
In Bandpass Sigma Delta Modulators a far 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 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 houses 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 filter out constitution must have adequate levels of freedom to enforce the specified (small-signal strong) 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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Extra resources for Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects
Compared to the expression for the SDM output in eq. 9), the input is additionally filtered with Gc,i(Z)/Gc,o(z). This provides additional degrees of freedom in the design of the zeroes of the STF. This can be easily seen by substituting G(z) = Gc,o(Z)/Gd(Z). 28) By adding the additional feedforward coefficients the zeroes of the STF are replaced: STF(z) = Gc,i(Z). 29) The additional freedom in the placement of the zeroes of the STF can be used to suppress unwanted signals in the input of the SDM at the expense of some extra hardware.
The output power of a one-bit quantizer is constant. Adding quantization noise with constant power to an input signal with variable power does not model the quantizer accurately. In order to accommodate the variable input, the quantizer can be modeled by an additive white noise source nq and a time invariant gain cg . The resulting model is shown in Fig. 1. In the case of a one-bit quantizer, the gain cg can have any value larger than zero. For multibit quantizers the value of cg will be near unity.
1 lists the values for the filter parameters and the resulting idle channel value for cg • The dynamic range of these modulators is shown in Fig. 3 and Fig. 4 as a function of the oversampling ratio OSR. For very low oversampling ratios (OSR < 4) a first order modulator achieves the highest dynamic range. When the OSR lies between OSR ~ 4 and OSR ~ 12 a second order modulator optimizes the DR. The requirements on the NTF pole placement for higher order modulators degrades their performance for such low oversampling ratios.
Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects by Jurgen van Engelen, Rudy J. van de Plassche