Transient simulation of complex electronic circuits and systems operating at ultra high frequencies

The electronics industry worldwide faces increasingly difficult challenges in a bid to produce ultra-fast, reliable and inexpensive electronic devices. Electronic manufacturers rely on the Electronic Design Automation (EDA) industry to produce consistent Computer A id e d Design (CAD) simulation tools that w ill enable the design of new high-performance integrated circuits (IC), the key component of a modem electronic device. However, the continuing trend towards increasing operational frequencies and shrinking device sizes raises the question of the capability of existing circuit simulators to accurately and efficiently estimate circuit behaviour. The principle objective of this thesis is to advance the state-of-art in the transient simulation of complex electronic circuits and systems operating at ultra high frequencies. Given a set of excitations and initial conditions, the research problem involves the determination of the transient response o f a high-frequency complex electronic system consisting of linear (interconnects) and non-linear (discrete elements) parts with greatly improved efficien cy compared to existing methods and with the potential for very high accuracy in a way that permits an effective trade-off between accuracy and computational complexity. High-frequency interconnect effects are a major cause of the signal degradation encountered b y a signal propagating through linear interconnect networks in the modem IC. Therefore, the development of an interconnect model that can accurately and efficiently take into account frequency-dependent parameters of modem non-uniform interconnect is of paramount importance for state-of-art circuit simulators. Analytical models and models based on a set of tabulated data are investigated in this thesis. Two novel, h igh ly accurate and efficient interconnect simulation techniques are developed. These techniques combine model order reduction methods with either an analytical resonant model or an interconnect model generated from frequency-dependent sparameters derived from measurements or rigorous full-wave simulation. The latter part o f the thesis is concerned with envelope simulation. The complex mixture of profoundly different analog/digital parts in a modern IC gives rise to multitime signals, where a fast changing signal arising from the digital section is modulated by a slower-changing envelope signal related to the analog part. A transient analysis of such a circuit is in general very time-consuming. Therefore, specialised methods that take into account the multi-time nature o f the signal are required. To address this issue, a novel envelope simulation technique is developed. This technique combines a wavelet-based collocation method with a multi-time approach to result in a novel simulation technique that enables the desired trade-off between the required accuracy and computational efficiency in a simple and intuitive way. Furthermore, this new technique has the potential to greatly reduce the overall design cycle

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Wavelet-based semiconductor device simulation.

by Pun Kong-Pang.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 94-[96]).Acknowledgement --- p.iAbstract --- p.iiiList of Tables --- p.viiList of Figures --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Role of Device Simulation --- p.2Chapter 1.2 --- Classification of Device Models --- p.3Chapter 1.3 --- Sections of a Typical Simulator --- p.6Chapter 1.4 --- Arrangement of This Thesis --- p.7Chapter 2 --- Classical Physical Model --- p.9Chapter 2.1 --- Carrier Densities --- p.12Chapter 2.2 --- Space Charge --- p.14Chapter 2.3 --- Carrier Mobilities --- p.15Chapter 2.4 --- Generation and Recombination --- p.17Chapter 2.5 --- Modeling of Device Boundaries --- p.20Chapter 2.6 --- Limits of Classical Device Modeling --- p.22Chapter 3 --- Computational Aspects --- p.23Chapter 3.1 --- Normalization --- p.24Chapter 3.2 --- Discretization --- p.26Chapter 3.2.1 --- Finite Difference Method --- p.26Chapter 3.2.2 --- Finite Element Method --- p.27Chapter 3.3 --- Nonlinear Systems --- p.28Chapter 3.3.1 --- Newton's Method --- p.28Chapter 3.3.2 --- Gummel's Method and its modification --- p.29Chapter 3.3.3 --- Comparison and discussion --- p.30Chapter 3.4 --- Linear System and Sparse Matrix --- p.32Chapter 4 --- Cubic Spline Wavelet Collocation Method for PDEs --- p.34Chapter 4.1 --- Cubic spline scaling functions and wavelets --- p.35Chapter 4.1.1 --- Approximation for a function in H2(I) --- p.43Chapter 4.2 --- Wavelet interpolation --- p.45Chapter 4.2.1 --- Interpolant operator Ivo in Vo --- p.45Chapter 4.2.2 --- Interpolation operator IWjf in Wj --- p.47Chapter 4.3 --- Derivative Matrices --- p.51Chapter 4.3.1 --- First derivative matrix --- p.51Chapter 4.3.2 --- Second derivative matrix --- p.53Chapter 4.4 --- Wavelet Collocation Method for Solving Device Equations --- p.55Chapter 4.4.1 --- Steady state solution --- p.57Chapter 4.4.2 --- Transient solution --- p.58Chapter 4.5 --- Reducing Collocation Points --- p.59Chapter 4.5.1 --- Error evaluation --- p.59Chapter 4.5.2 --- Deleting collocation points --- p.61Chapter 5 --- Numerical Results --- p.64Chapter 5.1 --- P-N Junction Diode --- p.64Chapter 5.1.1 --- Steady state solution --- p.69Chapter 5.1.2 --- Transient solution --- p.76Chapter 5.1.3 --- Convergence --- p.79Chapter 5.2 --- Bipolar Transistor --- p.81Chapter 5.2.1 --- Boundary Model --- p.82Chapter 5.2.2 --- DC Solution --- p.83Chapter 5.2.3 --- Transient Solution --- p.89Chapter 6 --- Conclusions --- p.92Bibliography --- p.9

Time-domain steady-state analysis of circuits with multiple adaptive grids

An effective adaptive algorithm to calculate the steady-state response of circuits is developed. This algorithm offers a powerful alternative to traditional steady-state simulation techniques, such as the shooting method or harmonic balance (HB). A favourable feature of the algorithm is that it obtains the unknown circuit solutions by using adaptive basis functions (ABF). The circuit equations are formulated by transformation matrices. One of the contributions of this thesis is to use the least squares method instead of Galerkin method to solve ordinary differential equations with ABF. Another contribution is that the proposed algorithm uses different grid resolutions to represent each state variable simultaneously. The position of the grid points for each state variable is adaptively controlled by an algorithm that attempts to minimize artifact oscillations in the solutions. The algorithm is demonstrated by simulating two circuits and comparing the results with Spice and Aplac

Analog Defect Injection and Fault Simulation Techniques: A Systematic Literature Review

Since the last century, the exponential growth of the semiconductor industry has led to the creation of tiny and complex integrated circuits, e.g., sensors, actuators, and smart power. Innovative techniques are needed to ensure the correct functionality of analog devices that are ubiquitous in every smart system. The ISO 26262 standard for functional safety in the automotive context specifies that fault injection is necessary to validate all electronic devices. For decades, standardization of defect modeling and injection mainly focused on digital circuits and, in a minor part, on analog ones. An initial attempt is being made with the IEEE P2427 draft standard that started to give a structured and formal organization to the analog testing field. Various methods have been proposed in the literature to speed up the fault simulation of the defect universe for an analog circuit. A more limited number of papers seek to reduce the overall simulation time by reducing the number of defects to be simulated. This literature survey describes the state-of-the-art of analog defect injection and fault simulation methods. The survey is based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodological flow, allowing for a systematic and complete literature survey. Each selected paper has been categorized and presented to provide an overview of all the available approaches. In addition, the limitations of the various approaches are discussed by showing possible future directions

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Rapid solution of potential integral equations in complicated 3-dimensional geometries

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 133-137).by Joel Reuben Phillips.Ph.D

Wavelet-based galerkin method for semiconductor device simulation.

by Chan Chung-Kei, Thomas.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 125-[129]).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 2 --- Semiconductor Device Physics --- p.5Chapter 2.1 --- IC Design Methodology --- p.6Chapter 2.1.1 --- System Level --- p.7Chapter 2.1.2 --- Circuit Level --- p.7Chapter 2.1.3 --- Device Level --- p.8Chapter 2.1.4 --- Process Level --- p.8Chapter 2.2 --- Classification of Device Models --- p.8Chapter 2.2.1 --- Circuit Models --- p.9Chapter 2.2.2 --- Physical Models --- p.10Chapter 2.3 --- Classical Drift-Diffusion model --- p.13Chapter 2.3.1 --- Basic Governing Equations in Semiconductors --- p.13Chapter 2.3.2 --- Shockley-Read-Hall Recombination Statics --- p.15Chapter 2.3.3 --- Boundary Conditions --- p.18Chapter 2.4 --- pn Junction at equilibrium --- p.20Chapter 2.4.1 --- The depletion approximation --- p.23Chapter 2.4.2 --- Current-voltage Characteristics --- p.26Chapter 3 --- Iteration Scheme --- p.30Chapter 3.1 --- Gummel's iteration scheme --- p.31Chapter 3.2 --- Modified Gummel's iteration scheme --- p.35Chapter 3.3 --- Solution of Differential Equation --- p.38Chapter 3.3.1 --- Finite Difference Method --- p.38Chapter 3.3.2 --- Moment Method --- p.39Chapter 4 --- Theory of Wavelets --- p.43Chapter 4.1 --- Multi-resolution Analysis --- p.43Chapter 4.1.1 --- Example of MRA with Haar Wavelet --- p.46Chapter 4.2 --- Orthonormal basis of Wavelets --- p.52Chapter 4.3 --- Fast Wavelet Transform --- p.56Chapter 4.4 --- Wavelets on the interval --- p.62Chapter 5 --- Galerkin-Wavelet Method --- p.66Chapter 5.1 --- Wavelet-based Moment Methods --- p.67Chapter 5.1.1 --- Wavelet transform on the stiffness matrix --- p.67Chapter 5.1.2 --- Wavelets as basis functions --- p.68Chapter 5.2 --- Galerkin-Wavelet method --- p.69Chapter 5.2.1 --- Boundary Conditions --- p.73Chapter 5.2.2 --- Adaptive Scheme --- p.74Chapter 5.2.3 --- The Choice of Classes of Wavelet Bases --- p.76Chapter 6 --- Numerical Results --- p.80Chapter 6.1 --- Steady State Solution --- p.81Chapter 6.1.1 --- Daubechies Wavelet N = 2 --- p.82Chapter 6.1.2 --- Daubechies Wavelet N=5 --- p.84Chapter 6.1.3 --- Discussion on Daubechies wavelets N = 2 and N=5 --- p.86Chapter 6.2 --- Transient Solution --- p.91Chapter 6.3 --- Convergence --- p.99Chapter 7 --- Conclusion --- p.103Chapter A --- Derivation for steady state --- p.107Chapter A.1 --- Generalized Moll-Ross Relation --- p.107Chapter A.2 --- Linearization of PDEs --- p.110Chapter B --- Derivation for transient state --- p.113Chapter C --- Notation --- p.119Chapter D --- Elements in the Stiffness Matrix --- p.122Bibliography --- p.12