Lossy transmission line response via numerical Laplace transform inversion

An efficient transient analysis of lossy lines with nonlinear loads requires the ability to compute and represent a suitable set of line impulse responses. In this paper, we propose the evaluation of the matched-line impulse responses by means of an algorithm for the numerical inversion of the Laplace transform. Based on a discussion of the structure of the impulse responses, we demonstrate how, for this class of functions, the method proposed is particularly effective and convenient, in comparison with the conventional FFT approach. We also compare the line responses due to the exact per-unit-length resistance of a circular wire with those due to a simplified model, and find a non-negligible influence on the integrity of the signals that propagate on the lin

Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc

Transient simulation of lossy multiconductor interconnects

The transient simulation of electrically-long low-loss multiconductor interconnects is considered from a practical point of view. The importance of frequency dependent losses in these interconnects is discussed and a simple transmission line characterization procedure allowing for such losses is proposed. The characterization obtained yields simple and efficient interconnect models, that the user can include, without programming, in any simulator accepting differential operator

Influence of the line characterization on the transient analysis of nonlinearly loaded lossy transmission lines

The analysis of nonlinearly terminated lossy transmission lines is addressed in this paper with a modified version of a method belonging to the class of mixed techniques, which characterize the line in the frequency domain and solve the nonlinear problem in the time domain via a convolution operation. This formulation is based on voltage wave variables defined in the load sections. The physical meaning of such quantities helps to explain the transient scattering process in the line and allows us to discover the importance (so far often overlooked) of the reference impedance used to define the scattering parameters. The complexity of the transient impulse responses, the efficiency of the algorithms, and the precision of the results are shown to be substantially conditioned by the choice of the reference impedance. The optimum value of the reference impedance depends on the amount of line losses. We show that a low-loss line can be effectively described if its characteristic impedance or the characteristic impedance of the associated LC line is chosen as the reference impedance. Based on the physical interpretation of our formulation, we are able to validate the numerical results, and to demonstrate that, despite claimed differences or improvements, the formulations of several mixed methods are fundamentally equivalen

Self-Validated Time-Domain Analysis of Linear Systems with Bounded Uncertain Parameters

This paper presents a novel approach to predict the bounds of the time-domain response of a linear system subject to multiple bounded uncertain input parameters. The method leverages the framework of Taylor models in conjunction with the numerical inversion of Laplace transform (NILT). Different formulations of the NILT are reviewed, and their advantages and limitations are discussed. An implementation relying on an inverse fast Fourier transform (IFFT) turns out to be the most efficient and accurate alternative. The feasibility of the technique is validated based on several diverse application examples, namely a control loop, a lossy transmission-line network and an active low-pass filter

Stability, Causality, and Passivity in Electrical Interconnect Models

Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically.We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itsel

Differential-difference equations for the transient simulation of lossy MTLs

In this paper, we address the differential representation of the time-domain characteristics of lossy MTLs. This approach is of great interest for the efficient simulation of circuits with long interconnects and nonlinearities. The properties of this characterization method are discussed with particular emphasis on the bandwidth and on the order of the differential operators used. Our discussion is supported by a complete characterization example for a realistic wideband 3-conductor interconnec

Delay Extraction based Macromodeling with Parallel Processing for Efficient Simulation of High Speed Distributed Networks

This thesis attempts to address the computational demands of accurate modeling of high speed distributed networks such as interconnect networks and power distribution networks. In order to do so, two different approaches towards modeling of high speed distributed networks are considered. One approach deals with cases where the physical characteristics of the network are not known and the network is characterized by its frequency domain tabulated data. Such examples include long interconnect networks described by their Y parameter data. For this class of problems, a novel delay extraction based IFFT algorithm has been developed for accurate transient response simulation. The other modeling approach is based on a detailed knowledge of the physical and electrical characteristics of the network and assuming a quasi transverse mode of propagation of the electromagnetic wave through the network. Such problems may include two dimensional (2D) and three dimensional (3D) power distribution networks with known geometry and materials. For this class of problem, a delay extraction based macromodeling approaches is proposed which has been found to be able to capture the distributed effects of the network resulting in more compact and accurate simulation compared to the state-of-the-art quasi-static lumped models. Furthermore, waveform relaxation based algorithms for parallel simulations of large interconnect networks and 2D power distribution networks is also presented. A key contribution of this body of work is the identification of naturally parallelizable and convergent iterative techniques that can divide the computational costs of solving such large macromodels over a multi-core hardware