By Jurgen van Engelen, Rudy J. van de Plassche
Sigma delta modulation has turn into a truly beneficial and largely utilized approach for top functionality Analog-to-Digital (A/D) conversion of slender band signs. by using oversampling and destructive suggestions, the quantization blunders of a rough quantizer are suppressed in a slender 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 service, as happens in verbal exchange structures resembling AM/FM receivers and cellphones.
a result of nonlinearity of the quantizer within the suggestions loop, a sigma delta modulator could show enter sign established balance homes. a similar mix of the nonlinearity and the suggestions loop complicates the soundness research. In Bandpass Sigma DeltaModulators, the describing functionality procedure is used to research the steadiness of the sigma delta modulator. The linear achieve version conventional for the quantizer fails to foretell small sign balance houses and idle styles competently.
In Bandpass Sigma Delta Modulators a more robust version for the quantizer is brought, extending the linear achieve version with a part shift. research indicates 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 actual 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 should be of curiosity to practising engineers and researchers within the parts 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
51 Bandpass Sigma Delta Modulators 80 ....................................... 11: Simulated and predicted SNR of a second orderlowpass SDM. in the SNR is located at -57dB relative to the quantizer output power q2/4. Because this "second-order" behavior of the tones can also be found in third and higher order modulators. the noticeable drop in SNR will also be present in the corresponding SNR vs. input power characteristics (see for example , p. 147). In Fig. 12 this characteristic is shown for a third order lowpass modulator.
2: Idle pattern of a first order lowpass modulator. k o[k] x[k] 0 '1. _'1. xo xO-1 2 2 5 2 3 4 '1. ry xo Xo": xo Xo": ry 2 1 2 1 initial state Xo and is worst for Xo = 0 or xo = q/2. The threshold value for the sum of the input samples then equals q/2. s, the sum of the input samples can be approximated by L ilk] K k=O l1 Ts ~ - when K» 1 and fs KTs 1=0 » AI . 17) f;. 18) In the case that this absolute maximum does not exceed the value of~, the idle pattern will not be disturbed. 19) The dead-zone of a first-order SDM is most noticeable for input signals with a relatively high (in-band) frequency.
G. 17: SDM with continuous time loop jilter. g. o[k]. Similarly, the Laplace transform G(p) is used to represent the continuous time loop filter transfer function. The continuous time transfer function of the DAC in the feedback loop is indicated by R(p). Although the loop filter is continuous time, the overall behavior of the SDM can be described by discrete time transfer functions . The loop filter and the DAC can be replaced by an equivalent discrete time filter G(z), which depends on the continuous time loop filter transfer function G(p), the DAC transfer function R(p) and the sample frequency Is.
Bandpass Sigma Delta Modulators: Stability Analysis, Performance and Design Aspects by Jurgen van Engelen, Rudy J. van de Plassche