Delta Sigma Modulators

This new edition introduces operation and design techniques for Sigma-Delta converters in physical and conceptual terms, and includes chapters which explore developments in the field over the last decade Includes information on MASH architectures, digital-to-analog converter (DAC) mismatch and mismatch shaping Investigates new topics including continuous-time ΔΣ analog-to-digital converters (ADCs) principles and designs, circuit design for both continuous-time and discrete-time ΔΣ ADCs, decimation and interpolation filters, and incremental ADCs Provides emphasis on practical design issues for industry professionals

This book describes several Digital Delta-Sigma Modulator (DDSM) architectures, including multi stage noise shaping (MASH), error feedback modulator (EFM) and single quantizer (SQ)-DDSM modulators, with a focus on predicting and maximizing their cycle lengths. The authors aim to demystify an important aspect of these particular DDSM structures, namely the existence of spurs resulting from the inherent periodicity of DDSMs with constant inputs. Simulink and MATLAB models and code are presented in Chapters 2–5 to enable the reader to reproduce the results in this work and to explore further. These examples will also be helpful for first-time designers of DDSMs.

Among analog-to-digital converters, the delta-sigma modulator has cornered the market on high to very high resolution converters at moderate speeds, with typical applications such as digital audio and instrumentation. Interest has recently increased in delta-sigma circuits built with a continuous-time loop filter rather than the more common switched-capacitor approach. Continuous-time delta-sigma modulators offer less noisy virtual ground nodes at the input, inherent protection against signal aliasing, and the potential to use a physical rather than an electrical integrator in the first stage for novel applications like accelerometers and magnetic flux sensors. More significantly, they relax settling time restrictions so that modulator clock rates can be raised. This opens the possibility of wideband (1 MHz or more) converters, possibly for use in radio applications at an intermediate frequency so that one or more stages of mixing might be done in the digital domain. Continuous-Time Delta-Sigma Modulators for High-Speed A/D Conversion: Theory, Practice and Fundamental Performance Limits covers all aspects of continuous-time delta-sigma modulator design, with particular emphasis on design for high clock speeds. The authors explain the ideal design of such modulators in terms of the well-understood discrete-time modulator design problem and provide design examples in Matlab. They also cover commonly-encountered non-idealities in continuous-time modulators and how they degrade performance, plus a wealth of material on the main problems (feedback path delays, clock jitter, and quantizer metastability) in very high-speed designs and how to avoid them. They also give a concrete design procedure for a real high-speed circuit which illustrates the tradeoffs in the selection of key parameters. Detailed circuit diagrams, simulation results and test results for an integrated continuous-time 4 GHz band-pass modulator for A/D conversion of 1 GHz analog signals are also presented. Continuous-Time Delta-Sigma Modulators for High-Speed A/D Conversion: Theory, Practice and Fundamental Performance Limits concludes with some promising modulator architectures and a list of the challenges that remain in this exciting field.

This important book deals with the modeling and design of higher-order single-stage delta-sigma modulators. It provides an overview of the architectures, the quantizer models, the design techniques and the implementation issues encountered in the study of the delta-sigma modulators. A number of applications are discussed, with emphasis on use in the design of analog-to-digital converters and in frequency synthesis. The book is education- rather than research-oriented, containing numerical examples and unsolved problems. It is aimed at introducing the final-year undergraduate, the graduate student or the electronic engineer to this field. Contents: Analog to Digital Conversion; ou Modulators OCo Architectures; Single-Bit Single-Stage ou Modulators, Modeling and Design; Implementation of ou Modulators; Practical Limitations of ou Modulators; Stabilization and Suppression of Tones for the Higher-Order Single-Stage ou Modulators; Decimation, Interpolation and Converters; Applications. Readership: Final-year undergraduates; graduate students; electrical, electronic and systems engineers."

The interest for :I:~ modulation-based NO converters has significantly increased in the last years. The reason for that is twofold. On the one hand, unlike other converters that need accurate building blocks to obtain high res olution, :I:~ converters show low sensitivity to the imperfections of their building blocks. This is achieved through extensive use of digital signal pro cessing - a desirable feature regarding the implementation of NO interfaces in mainstream CMOS technologies which are better suited for implementing fast, dense, digital circuits than accurate analog circuits. On the other hand, the number of applications with industrial interest has also grown. In fact, starting from the earliest in the audio band, today we can find :I:~ converters in a large variety of NO interfaces, ranging from instrumentation to commu nications. These advances have been supported by a number of research works that have lead to a considerably large amount of published papers and books cov ering different sub-topics: from purely theoretical aspects to architecture and circuit optimization. However, so much material is often difficultly digested by those unexperienced designers who have been committed to developing a :I:~ converter, mainly because there is a lack of methodology. In our view, a clear methodology is necessary in :I:~ modulator design because all related tasks are rather hard.

Sigma delta modulation has become a very useful and widely applied technique for high performance Analog-to-Digital (A/D) conversion of narrow band signals. Through the use of oversampling and negative feedback, the quantization errors of a coarse quantizer are suppressed in a narrow signal band in the output of the modulator. Bandpass sigma delta modulation is well suited for A/D conversion of narrow band signals modulated on a carrier, as occurs in communication systems such as AM/FM receivers and mobile phones. Due to the nonlinearity of the quantizer in the feedback loop, a sigma delta modulator may exhibit input signal dependent stability properties. The same combination of the nonlinearity and the feedback loop complicates the stability analysis. In Bandpass Sigma Delta Modulators, the describing function method is used to analyze the stability of the sigma delta modulator. The linear gain model commonly used for the quantizer fails to predict small signal stability properties and idle patterns accurately. In Bandpass Sigma Delta Modulators an improved model for the quantizer is introduced, extending the linear gain model with a phase shift. Analysis shows that the phase shift of a sampled quantizer is in fact a phase uncertainty. Stability analysis of sigma delta modulators using the extended model allows accurate prediction of idle patterns and calculation of small-signal stability boundaries for loop filter parameters. A simplified rule of thumb is derived and applied to bandpass sigma delta modulators. The stability properties have a considerable impact on the design of single-loop, one-bit, high-order continuous-time bandpass sigma delta modulators. The continuous-time bandpass loop filter structure should have sufficient degrees of freedom to implement the desired (small-signal stable) sigma delta modulator behavior. Bandpass Sigma Delta Modulators will be of interest to practicing engineers and researchers in the areas of mixed-signal and analog integrated circuit design.

Oversampled Delta-Sigma Modulators: Analysis, Applications, and Novel Topologies presents theorems and their mathematical proofs for the exact analysis of the quantization noise in delta-sigma modulators. Extensive mathematical equations are included throughout the book to analyze both single-stage and multi-stage architectures. It has been proved that appropriately set initial conditions generate tone free output, provided that the modulator order is at least three. These results are applied to the design of a Fractional-N PLL frequency synthesizer to produce spurious free RF waveforms. Furthermore, the book also presents time-interleaved topologies to increase the conversion bandwidth of delta-sigma modulators. The topologies have been generalized for any interleaving number and modulator order. The book is full of design and analysis techniques and contains sufficient detail that enables readers with little background in the subject to easily follow the material in it.