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The current technological progress in microelectronics is driven by the desire to decrease feature sizes, increase frequencies and the need for low supply voltages. Amongst other effects the signal-to-noise ratio decreases and the transient noise analysis becomes necessary in the simulation of electronic circuits. Taking the inner electronic noise into account by means of Gaussian white noise currents, mathematical modelling leads to stochastic differential algebraic equations (SDAEs) with a large number of small noise sources. The simulation of such systems requires an efficient numerical time integration by mean-square convergent numerical methods. In this thesis, adaptive linear multi-step Maruyama schemes to solve stochastic differential equations (SDEs) and SDAEs are developed. A reliable local error estimate for systems with small noise is provided and a strategy for controlling the step-size and the number of solution paths simultaneously in one approximation is presented. Numerical experiments on industrial relevant real-life applications illustrate the theoretical findings.
This book is about the results of a number of projects funded by the BMBF in the initiative "Mathematics for Innovations in Industry and Services". It shows that a broad spectrum of analytical and numerical mathematical methods and programming techniques are used to solve a lot of different specific industrial or services problems. The main focus is on the fact that the mathematics used is not usually standard mathematics or black box mathematics but is specifically developed for specific industrial or services problems. Mathematics is more than a tool box or an ancilarry science for other scientific disciplines or users. Through this book the reader will gain insight into the details of mathematical modeling and numerical simulation for a lot of industrial applications.
This book is a collection of papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sicily, in 2004. The series of SCEE conferences aims at addressing mathematical problems which have a relevancy to industry. The areas covered at SCEE-2004 were: Electromagnetism, Circuit Simulation, Coupled Problems and General mathematical and computational methods.
This book shows how modern Applied Mathematics influences everyday life. It features contributors from universities, research institutions and industry, who combine research and review papers to present a survey of current research. More than 20 contributions are divided into scales: nano, micro, macro, space and real life. In addition, coverage includes engaging and informative case studies as well as complex graphics and illustrations, many of them in color.
This work is dedicated to CMOS based imaging with the emphasis on the noise modeling, characterization and optimization in order to contribute to the design of high performance imagers in general and range imagers in particular. CMOS is known to be superior to CCD due to its flexibility in terms of integration capabilities, but typically has to be enhanced to compete at parameters as for instance noise, dynamic range or spectral response. This work gathers the widespread theory on noise and extends the theory by a non-rigorous but potentially computing efficient algorithm to estimate noise in time sampled systems.
In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand the purpose of their own existence and the universe. They built a supercomputer, called Deep Thought, and upon completion, they asked it for the answer to the ultimate question of life, the universe and everything else. The computer worked for several millennia on the answers to all these questions. When the day arrived for hyper-intelligent beings the to receive the answer, they were stunned, shocked and disappointed to hear that the answer was simply 42. The still open questions to scientists and engineers are typically much sim pler and consequently the answers are more reasonable. Furthermore, because human beings are too impatient and not ready to wait for such a long pe riod, high-performance computing techniques have been developed, leading to much faster answers. Based on these developments in the last two decades, scientific and engineering computing has evolved to a key technology which plays an important role in determining, or at least shaping, future research and development activities in many branches of industry. Development work has been going on all over the world resulting in numerical methods that are now available for simulations that were not foreseeable some years ago. However, these days the availability of supercomputers with Teraflop perfor mance supports extensive computations with technical relevance. A new age of engineering has started.
This thesis provides a thorough noise analysis for conventional CIS readout chains, while also presenting and discussing a variety of noise reduction techniques that allow the read noise in standard processes to be optimized. Two physical implementations featuring sub-0.5-electron RMS are subsequently presented to verify the proposed noise reduction techniques and provide a full characterization of a VGA imager. Based on the verified noise calculation, the impact of the technology downscaling on the input-referred noise is also studied. Further, the thesis covers THz CMOS image sensors and presents an original design that achieves ultra-low-noise performance. Last but not least, it provides a comprehensive review of CMOS image sensors.
In electronic circuit and system design, the word noise is used to refer to any undesired excitation on the system. In other contexts, noise is also used to refer to signals or excitations which exhibit chaotic or random behavior. The source of noise can be either internal or external to the system. For instance, the thermal and shot noise generated within integrated circuit devices are in ternal noise sources, and the noise picked up from the environment through electromagnetic interference is an external one. Electromagnetic interference can also occur between different components of the same system. In integrated circuits (Ies), signals in one part of the system can propagate to the other parts of the same system through electromagnetic coupling, power supply lines and the Ie substrate. For instance, in a mixed-signal Ie, the switching activity in the digital parts of the circuit can adversely affect the performance of the analog section of the circuit by traveling through the power supply lines and the substrate. Prediction of the effect of these noise sources on the performance of an electronic system is called noise analysis or noise simulation. A methodology for the noise analysis or simulation of an electronic system usually has the following four components: 2 NOISE IN NONLINEAR ELECTRONIC CIRCUITS • Mathematical representations or models for the noise sources. • Mathematical model or representation for the system that is under the in fluence of the noise sources.
This book is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and physicists, with the goal of intensive discussions on industrially relevant mathematical problems, with an emphasis on modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems.This extensive reference work is divided into five parts: 1. Computational electromagnetics, 2. Circuit simulation, 3. Coupled problems, 4. Mathematical and computational methods, and 5. Model-order reduction. Each part starts with an general introduction followed by the actual papers.