Time-Domain Macromodeling of High Speed Distributed Networks

With the rapid growth in density, operating speeds and complexity of modern very-large-scale integration (VLSI) circuits, there is a growing demand on efficient and accurate modeling and simulation of high speed interconnects and packages in order to ensure the signal integrity, reliability and performance of electronic systems. Such models can be derived from the knowledge of the physical characteristics of the structure or based on the measured port-to-port response.In the first part of this thesis, a passive macromodeling technique based on Method of Characteristics (referred as Passive Method of Characteristics or PMoC) is described which is applicable for modeling of electrically long high-speed interconnect networks. This algorithm is based on extracting the propagation delay of the interconnect followed by a low order rational approximation to capture the attenuation effects. The key advantage of the algorithm is that the curve fitting to realize the macromodel depends only on per-unit-length (p.u.l.) parameters and not on the length of the transmission line. In this work, the PMoC is developed to model multiconductor transmission lines.Next, an efficient approach for time domain sensitivity analysis of lossy high speed interconnects in the presence of nonlinear terminations is presented based on PMoC. An important feature of the proposed method is that the sensitivities are obtained from the solution of the original network, leading to significant computational advantages. The sensitivity analysis is also used to optimize the physical parameters of the network to satisfy the required design constraints. A time-domain macromodel for lossy multiconductor transmission lines exposed to electromag¬netic interference is also described in this thesis based on PMoC. The algorithm provides an efficient mechanism to ensure the passivity of the macromodel for different line lengths. Numerical examples illustrate that when compared to other passive incident field coupling algorithms, the proposed method is efficient in modeling electrically long interconnects since delay extraction without segmentation is used to capture the frequency response.In addition, this thesis discusses macromodeling techniques for complex packaging structures based on the frequency-domain behavior of the system obtained from measurements or electromagnetic simulators. Such techniques approximate the transfer function of the interconnect network as a rational function which can be embedded with modern circuit simulators with integrated circuit emphasis (SPICE). One of the most popular tools for rational approximations of measured or simulated data is based on vector fitting (VF) algorithms. Nonetheless, the vector fitting algorithms usually suffer convergence issues and lack of accuracy when dealing with noisy measured data. As a part of this thesis, a methodology is presented to improve the convergence and accuracy issues of vector fitting algorithm based on instrumental variable technique. This methodology is based on obtaining the “instruments” in an iterative manner and do not increase the complexity of vector fitting to capture the frequency response and minimize the biasing

Time-domain Analysis of Multiconductor Transmission Lines Excited by Transient Electromagnetic Disturbances Based on the Analog Behavior Modeling

L'abstract è presente nell'allegato / the abstract is in the attachmen

Analysis of nonuniform transmission lines with an iterative and adaptive perturbation technique

This paper presents an iterative and adaptive perturbation technique for the analysis of nonuniform transmission lines. Place-dependent variations of the per-unit-length parameters are interpreted as perturbations with respect to their average values along the line. This allows casting the governing equations for the corresponding perturbations of the voltages and currents as those of a uniform transmission line with distributed sources. Therefore, standard transmission line theory is used to calculate these perturbation terms. Specifically, perturbations of increasing order are computed iteratively starting from the solution of the unperturbed line. The accuracy is adaptively adjusted by setting a threshold on the convergence of the solution. The algorithm turns out to be simple to implement and very accurate, yet faster than traditional approaches based on the discretization of the line into uniform sections. The technique is validated through the analysis of several nonuniform transmission line structures of relevance in EMC applications, namely uniformly and nonuniformly twisted wire pairs as well as a cable bundle with lacing cords

Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

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

BGA footprints modeling and physics based via models validation for power and signal integrity applications

Modeling and simulating the multi-scale nature of a power distribution network (PDN) is essential to ensure the correct functioning of the devices connected to it. Simple parallel-plate sections constitute the core of these PDN geometries, together with sections where a large number of holes and vias are present, as in the case of a BGA footprint. Employing a divide-and-conquer approach allows for the modeling of these geometries separately, i.e., 3-D full wave solvers for the sections with holes and vias, and a cavity model approach, for the simple parallel-plate structures. Also, equivalent circuit models can be obtained for time-domain and frequency-domain SPICE simulations --Abstract, page iv

Time-domain modeling of high-frequency electromagnetic wave propagation, overhead wires, and earth

Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished. Prediction of radiated fields from transmission lines has not previously been studied from a panoptical power system perspective. The application of BPL technologies to overhead transmission lines would benefit greatly from an ability to simulate real power system environments, not limited to the transmission lines themselves. Presently circuitbased transmission line models used by EMTP-type programs utilize Carson’s formula for a waveguide parallel to an interface. This formula is not valid for calculations at high frequencies, considering effects of earth return currents. This thesis explains the challenges of developing such improved models, explores an approach to combining circuit-based and electromagnetics modeling to predict radiated fields from transmission lines, exposes inadequacies of simulation tools, and suggests methods of extending the validity of transmission line models into very high frequency ranges. Electromagnetics programs are commonly used to study radiated fields from transmission lines. However, an approach is proposed here which is also able to incorporate the components of a power system through the combined use of EMTP-type models. Carson’s formulas address the series impedance of electrical conductors above and parallel to the earth. These equations have been analyzed to show their inherent assumptions and what the implications are. Additionally, the lack of validity into higher frequencies has been demonstrated, showing the need to replace Carson’s formulas for these types of studies. This body of work leads to several conclusions about the relatively new study of BPL. Foremost, there is a gap in modeling capabilities which has been bridged through integration of circuit-based and electromagnetics modeling, allowing more realistic prediction of BPL performance and radiated fields. The proposed approach is limited in its scope of validity due to the formulas used by EMTP-type software. To extend the range of validity, a new set of equations must be identified and implemented in the approach. Several potential methods of implementation have been explored. Though an appropriate set of equations has not yet been identified, further research in this area will benefit from a clear depiction of the next important steps and how they can be accomplished

Uncertainty Quantification of the Responses of Transient Electromagnetic Disturbance Coupling to Transmission Lines Based on Stochastic Models

L'abstract è presente nell'allegato / the abstract is in the attachmen