An efficient numerical algorithm for the transient analysis of high-frequency non-linear circuits

The paper proposes a new approach for the discrete-time integration of non-linear differential equations that describe the behaviour of high-frequency circuits, in particular those containing complex equivalent-circuit models of microwave transistor devices. The proposed approach reformulates a conventional predictor-corrector method in terms of Pad�© approximates about each function sample. The method is especially suited to the kind of non-linear stiff differential equations that arise frequently in high-frequency analysis

Time-domain analysis of large-scale circuits by matrix exponential method with adaptive control

We propose an explicit numerical integration method based on matrix exponential operator for transient analysis of large-scale circuits. Solving the differential equation analytically, the limiting factor of maximum time step changes largely from the stability and Taylor truncation error to the error in computing the matrix exponential operator. We utilize Krylov subspace projection to reduce the computation complexity of matrix exponential operator. We also devise a prediction-correction scheme tailored for the matrix exponential approach to dynamically adjust the step size and the order of Krylov subspace approximation. Numerical experiments show the advantages of the proposed method compared with the implicit trapezoidal method. © 1982-2012 IEEE.published_or_final_versio

Nano-Sim: A Step Wise Equivalent Conductance based Statistical Simulator for Nanotechnology Circuit Design

New nanotechnology based devices are replacing CMOS devices to overcome CMOS technology's scaling limitations. However, many such devices exhibit non-monotonic I-V characteristics and uncertain properties which lead to the negative differential resistance (NDR) problem and the chaotic performance. This paper proposes a new circuit simulation approach that can effectively simulate nanotechnology devices with uncertain input sources and negative differential resistance (NDR) problem. The experimental results show a 20-30 times speedup comparing with existing simulators.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

Parallel Algorithms for Time and Frequency Domain Circuit Simulation

As a most critical form of pre-silicon verification, transistor-level circuit simulation is an indispensable step before committing to an expensive manufacturing process. However, considering the nature of circuit simulation, it can be computationally expensive, especially for ever-larger transistor circuits with more complex device models. Therefore, it is becoming increasingly desirable to accelerate circuit simulation. On the other hand, the emergence of multi-core machines offers a promising solution to circuit simulation besides the known application of distributed-memory clustered computing platforms, which provides abundant hardware computing resources. This research addresses the limitations of traditional serial circuit simulations and proposes new techniques for both time-domain and frequency-domain parallel circuit simulations. For time-domain simulation, this dissertation presents a parallel transient simulation methodology. This new approach, called WavePipe, exploits coarse-grained application-level parallelism by simultaneously computing circuit solutions at multiple adjacent time points in a way resembling hardware pipelining. There are two embodiments in WavePipe: backward and forward pipelining schemes. While the former creates independent computing tasks that contribute to a larger future time step, the latter performs predictive computing along the forward direction. Unlike existing relaxation methods, WavePipe facilitates parallel circuit simulation without jeopardizing convergence and accuracy. As a coarse-grained parallel approach, it requires low parallel programming effort, furthermore it creates new avenues to have a full utilization of increasingly parallel hardware by going beyond conventional finer grained parallel device model evaluation and matrix solutions. This dissertation also exploits the recently developed explicit telescopic projective integration method for efficient parallel transient circuit simulation by addressing the stability limitation of explicit numerical integration. The new method allows the effective time step controlled by accuracy requirement instead of stability limitation. Therefore, it not only leads to noticeable efficiency improvement, but also lends itself to straightforward parallelization due to its explicit nature. For frequency-domain simulation, this dissertation presents a parallel harmonic balance approach, applicable to the steady-state and envelope-following analyses of both driven and autonomous circuits. The new approach is centered on a naturally-parallelizable preconditioning technique that speeds up the core computation in harmonic balance based analysis. The proposed method facilitates parallel computing via the use of domain knowledge and simplifies parallel programming compared with fine-grained strategies. As a result, favorable runtime speedups are achieved

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

Evaluation of numerical methods for TSCOPF in a large interconnected system

Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of power systems. However, they require a high computational effort and can suffer from convergence problems when applied to large systems. This study analyzes the performance of eleven numerical integration algorithms applied to ordinary differential equations that represent power system dynamics in a TSCOPF model. The analyzed algorithms cover a range of explicit and implicit methods, including the recently published semi-explicit and semi-implicit Adams-Bashforth-Moulton formulas, together with several initialization techniques. The integration methods are applied to a model of the Iberian Peninsula power system, and their performance is discussed in terms of convergence, accuracy, and computational effort. The results show that most implicit methods converge to the solution, even for large time steps. In particular, the Adams-Moulton method of order two and Simpson's rule, both initialized with RK4, outperform the trapezoidal rule, which is the default method in TSCOPF models.This work was supported by the Spanish Agencia Estatal de Investigación under Project PID2019-104449RB-I00 and Project AEI/10.13039/501100011033

Efficient Macromodeling and Fast Transient Simulation of High Speed Distributed Interconnects

In the first part of the thesis, an efficient macromodeling technique based on Loewner Matrix (LM) approach has been presented to model multi-port distributed systems using tabulated noisy data. In the proposed method, Loewner Model data from previous rational approximation are used to create less noisy eigenvectors in an iterative manner. As a result, the biasing effect of the LM model approximated by the noisy data is reduced. It is illustrated that this method improves the accuracy of the Loewner Matrix modeling for noisy frequency data. In the second part, a fast and robust algorithm is introduced for time-domain simulation of interconnects with few nonlinear elements based on Large Change Sensitivity approach. After macromodeling interconnects, linear parts of the system construct very large matrix. Large linear matrix with nonlinear components makes time domain simulation a Central Processing Unit (CPU) intensive task where inversion (one Lower/Upper (LU) decomposition and one forward/backward substitution) of this large matrix is done at each step of the Newton-Raphson iteration. Using the proposed method, large system matrix is partitioned into linear and nonlinear parts and LU decomposition of linear matrix is done only once in the entire simulation. Nonlinear elements construct a very small matrix compared to large linear matrix. In this proposed method, small matrix is inverted at each Newton iteration. Cost of inverting a small matrix is much cheaper than inverting a very large matrix. Therefore, this approach is faster than the conventional matrix inversion method. Numerical examples are presented illustrating validity and efficiency of the above method

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

Status of the differential transformation method

Further to a recent controversy on whether the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used, often only, as a technique for (analytically) calculating the power series of the solution (in terms of the initial value parameters). Sometimes, a piecewise analytic continuation process is implemented either in a numerical routine (e.g., within a shooting method) or in a semi-analytical procedure (e.g., to solve a boundary value problem). Emphasized also is the fact that, at the time of its invention, the currently-used basic ingredients of the DTM (that transform a differential equation into a difference equation of same order that is iteratively solvable) were already known for a long time by the "traditional"-Taylor-method users (notably in the elaboration of software packages --numerical routines-- for automatically solving ordinary differential equations). At now, the defenders of the DTM still ignore the, though much better developed, studies of the "traditional"-Taylor-method users who, in turn, seem to ignore similarly the existence of the DTM. The DTM has been given an apparent strong formalization (set on the same footing as the Fourier, Laplace or Mellin transformations). Though often used trivially, it is easily attainable and easily adaptable to different kinds of differentiation procedures. That has made it very attractive. Hence applications to various problems of the Taylor method, and more generally of the power series method (including noninteger powers) has been sketched. It seems that its potential has not been exploited as it could be. After a discussion on the reasons of the "misunderstandings" which have caused the controversy, the preceding topics are concretely illustrated.Comment: To appear in Applied Mathematics and Computation, 29 pages, references and further considerations adde