By Lucien Breems, Johan Huijsing
This textual content describes the layout and concept of continuous-time sigma-delta modulators for analogue-to-digital conversion in radio receivers. The book's major concentration is on dynamic variety, linearity and tool potency facets of sigma-delta modulators, that are extremely important specifications to be used in battery operated receivers.
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Extra resources for Continuous-time Sigma-Delta modulation for A/D conversion in radio receivers
3-18 shows that the poles move into the right-half plane with increasing quantizer gain The poles move back into the left-half plane if the gain decreases. This may result in a stable periodic sequence, or limit cycle, at the output of the modulator. A limit cycle occurs if the closed-loop gain is 1 phase shift in the loop is CONTINUOUS-TIME MODULATION FOR A/D CONVERSION IN RADIO RECEIVERS 49 Continuous-time sigma-delta modulation The gain and phase shift of the loopfilter and the zero-order hold function are determined for all frequencies.
An optimum can be found which provides both high frequency stability and second-order noise shaping at low frequencies. The choice for the coefficient value cannot be too critical to prevent process spread from pushing the modulator to instability. Using the quantizer model as described in Eq. (3-24), the characteristic equation of the system of Fig. 4 High-frequency stability compensation * The zero of Eq. (3-33) equals The root locus plot was shown in Fig. 3-18. Indeed, Eq. (3-34) shows that by increasing the value of relative to the loopfilter zero moves to lower frequencies which improves system stability at the cost of less effective noise-shaping (first-order behavior).
The error E due to the quantization process is the difference between the analog quantizer input signal and the quantized output. Suppression of the quantization error in a modulator is provided by two mechanisms: oversampling of the signal bandwidth and shaping of the noise by the loopfilter. Because the reduction of the quantization error by these mechanisms is so effective, a high-resolution digital output is obtained, using only a low-resolution quantizer. In the extreme case a one-bit quantizer with two output levels is sufficient.