Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is available at http://pydsm.googlecode.co

Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators

It is well known that second order lowpass interpolative sigma delta modulators (SDMs) may suffer from instability and limit cycle problems when the magnitudes of the input signals are at large and at intermediate levels, respectively. In order to solve these problems, we propose to replace the second order lowpass interpolative SDMs to a specific class of second order bandpass interpolative SDMs with the natural frequencies of the loop filters very close to zero. The global stability property of this class of second order bandpass interpolative SDMs is characterized and some interesting phenomena are discussed. Besides, conditions for the occurrence of limit cycle and fractal behaviors are also derived, so that these unwanted behaviors will not happen or can be avoided. Moreover, it is found that these bandpass SDMs may exhibit irregular and conical-like chaotic patterns on the phase plane. By utilizing these chaotic behaviors, these bandpass SDMs can achieve higher signal-to-noise ratio (SNR) and tonal suppression than those of the original lowpass SDMs

Adaptive design of delta sigma modulators

In this thesis, a genetic algorithm based on differential evolution (DE) is used to generate delta sigma modulator (DSM) noise transfer functions (NTFs). These NTFs outperform those generated by an iterative approach described by Schreier and implemented in the delsig Matlab toolbox. Several lowpass and bandpass DSMs, as well as DSM\u27s designed specifically for and very low intermediate frequency (VLIF) receivers are designed using the algorithm developed in this thesis and compared to designs made using the delsig toolbox. The NTFs designed using the DE algorithm always have a higher dynamic range and signal to noise ratio than those designed using the delsig toolbox

A design tool for high-resolution high-frequency cascade continuous- time Σ∆ modulators

Event: Microtechnologies for the New Millennium, 2007, Maspalomas, Gran Canaria, SpainThis paper introduces a CAD methodology to assist the de signer in the implementation of continuous-time (CT) cas- cade Σ∆ modulators. The salient features of this methodology ar e: (a) flexible behavioral modeling for optimum accuracy- efficiency trade-offs at different stages of the top-down synthesis process; (b) direct synthesis in the continuous-time domain for minimum circuit complexity and sensitivity; a nd (c) mixed knowledge-based and optimization-based architec- tural exploration and specification transmission for enhanced circuit performance. The applicability of this methodology will be illustrated via the design of a 12 bit 20 MHz CT Σ∆ modulator in a 1.2V 130nm CMOS technology.Ministerio de Ciencia y Educación TEC2004-01752/MICMinisterio de Industria, Turismo y Comercio FIT-330100-2006-134 SPIRIT Projec

Design, analysis and evaluation of sigma-delta based beamformers for medical ultrasound imaging applications

The inherent analogue nature of medical ultrasound signals in conjunction with the abundant merits provided by digital image acquisition, together with the increasing use of relatively simple front-end circuitries, have created considerable demand for single-bit beamformers in digital ultrasound imaging systems. Furthermore, the increasing need to design lightweight ultrasound systems with low power consumption and low noise, provide ample justification for development and innovation in the use of single-bit beamformers in ultrasound imaging systems. The overall aim of this research program is to investigate, establish, develop and confirm through a combination of theoretical analysis and detailed simulations, that utilize raw phantom data sets, suitable techniques for the design of simple-to-implement hardware efficient digital ultrasound beamformers to address the requirements for 3D scanners with large channel counts, as well as portable and lightweight ultrasound scanners for point-of-care applications and intravascular imaging systems. In addition, the stability boundaries of higher-order High-Pass (HP) and Band-Pass (BP) Σ−Δ modulators for single- and dual- sinusoidal inputs are determined using quasi-linear modeling together with the describing-function method, to more accurately model the modulator quantizer. The theoretical results are shown to be in good agreement with the simulation results for a variety of input amplitudes, bandwidths, and modulator orders. The proposed mathematical models of the quantizer will immensely help speed up the design of higher order HP and BP Σ−Δ modulators to be applicable for digital ultrasound beamformers. Finally, a user friendly design and performance evaluation tool for LP, BP and HP modulators is developed. This toolbox, which uses various design methodologies and covers an assortment of modulators topologies, is intended to accelerate the design process and evaluation of modulators. This design tool is further developed to enable the design, analysis and evaluation of beamformer structures including the noise analyses of the final B-scan images. Thus, this tool will allow researchers and practitioners to design and verify different reconstruction filters and analyze the results directly on the B-scan ultrasound images thereby saving considerable time and effort

Contribución al modelado y diseño de moduladores sigma-delta en tiempo continuo de baja relación de sobremuestreo y bajo consumo de potencia

Continuous-Time Sigma-Delta modulators are often employed as analog-to-digital converters. These modulators are an attractive approach to implement high-speed converters in VLSI systems because they have low sensitivity to circuit imperfections compared to other solutions. This work is a contribution to the analysis, modelling and design of high-speed Continuous-Time Sigma-Delta modulators. The resolution and the stability of these modulators are limited by two main factors, excess-loop delay and sampling uncertainty. Both factors, among others, have been carefully analysed and modelled. A new design methodology is also proposed. It can be used to get an optimum high-speed Continuous-Time Sigma-Delta modulator in terms of dynamic range, stability and sensitivity to sampling uncertainty. Based on the proposed design methodology, a software tool that covers the main steps has been developed. The methodology has been proved by using the tool in designing a 30 Megabits-per-second Continuous-Time Sigma-Delta modulator with 11-bits of dynamic range. The modulator has been integrated in a 0.13-µm CMOS technology and it has a measured peak SNR of 62.5dB

Prediction of the Spectrum of a Digital Delta–Sigma Modulator Followed by a Polynomial Nonlinearity

This paper presents a mathematical analysis of the power spectral density of the output of a nonlinear block driven by a digital delta-sigma modulator. The nonlinearity is a memoryless third-order polynomial with real coefficients. The analysis yields expressions that predict the noise floor caused by the nonlinearity when the input is constant