By Lucien Breems, Johan Huijsing
Continuous-Time Sigma-Delta Modulation for A/D Conversion in RadioReceivers describes the layout and conception of continuous-time sigma-delta modulators for analog-to-digital conversion in radio receivers. The book's major concentration is on dynamic variety, linearity and tool potency features of sigma-delta modulators, that are vitally important specifications to be used in battery operated receivers like GSM telephones. an enormous a part of the booklet bargains with the picture rejection functionality of quadrature sigma-delta modulators. it truly is proven that suggestions like dynamic-element-matching and integration of a mixer with the sigma-delta modulator vastly increase the functionality and performance. moreover, the authors give you the reader with a theoretical assessment of continuous-time sigma-delta modulation, together with non-ideal results, balance concerns and assorted filter out designs. The book's concluding chapters current chip realizations exhibiting sensible implementations of low-power and high-performance sigma-delta modulators for GSM and AM/FM radio applications.
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With this linear model the root locus method can be applied to analyze the linearized system for stable limit cycles. First, stability of a modulator in the case of a small input signal is discussed, followed by the large signal stability analysis. 1 Small signal stability Fig. 3-15 shows a linear model of a continuous-time (CT) modulator. The system consists of a CT loopfilter with transfer function H(s) and a sampled quantizer. The quantizer is modeled with a linear gain and a phase shift The quantizer output, which is a train of pulses, is fed back through a D/A converter, being a zero-order hold function, and subtracted from the analog input signal.
3-15 can be determined Due to the exponential terms in Eq. (3-27) there is no analytical expression which can solve this characteristic equation. 3-17). 3-17 shows that the poles which are starting from the origin, move directly into the right-half plane for any gain and any phase Hence, the linear model of a second-order modulator is unstable for any quantizer gain and phase. 3 Linear stability analysis Eq. 4). An example transfer function of such a second-order low-pass filter is given by The characteristic equation of the second-order system Fig.