Parametric macromodeling of lossy and dispersive multiconductor transmission lines

We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate orthonormal vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain

A global normal form for two-dimensional mode conversion

Mode conversion is a phenomenon that is of interest as a method for heating in fusion reactors. A magnetosonic wave with dispersion relation DMS propagates toward the interior of the plasma, where it excites an ion-hybrid wave with dispersion relation DIH and thereby transfers energy to the plasma. We wish to study this process using ray-based methods. The 2 2 dispersion matrix D, which is, in general, a function of the phase space variables (x; y; kx; ky), must be put into normal form, in which the diagonals of D, identied as the uncoupled dispersion relations, DMS and DIH, Poisson-commute with the o-diagonals, identied as the coupling constants. Once in this form, we look at the points in the four- dimensional phase space that satisfy DMS(x; y; kx; ky) = 0 = DIH(x; y; kx; ky), which, in general, will be a two-dimensional surface we call the conversion surface. We implement our normal form algorithm on two models. First, we consider a slab model, in which D depends only on (x; kx; ky). Then we consider a two-dimensional model of the polodial cross section of a tokamak reactor with a DT plasma with a density ratio of one- to-one. Using numerical methods, we put D into normal form and identify the conversion surface. For both models, we nd that there are regions in the four-dimensional phase space where the normal form transformation is well behaved and the conversion surface is what we expect. These are where the two dispersion surfaces DMS(x; y; kx; ky) = 0 and DIH(x; y; kx; ky) = 0 intersect transversely. However, there are also regions in the phase space where the normal form transformation is not well behaved. These coincide with tangential conversions, that is, where the two dispersion surfaces intersect tangentially. In this case, we must revisit the normal form theory and adapt it to this non-generic situation. Finally, we compute the transmission and conversion coecients for such tangential conversions

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

Addressing Computational Complexity of High Speed Distributed Circuits Using Model Order Reduction

Advanced in the fabrication technology of integrated circuits (ICs) over the last couple of years has resulted in an unparalleled expansion of the functionality of microelectronic systems. Today’s ICs feature complex deep-submicron mixed-signal designs and have found numerous applications in industry due to their lower manufacturing costs and higher performance levels. The tendency towards smaller feature sizes and increasing clock rates is placing higher demands on signal integrity design by highlighting previously negligible interconnect effects such as distortion, reflection, ringing, delay, and crosstalk. These effects if not predicted in the early stages of the design cycle can severely degrade circuit performance and reliability. The objective of this thesis is to develop new model order reduction (MOR) techniques to minimize the computational complexity of non-linear circuits and electronic systems that have delay elements. MOR techniques provide a mechanism to generate reduced order models from the detailed description of the original modified nodal analysis (MNA) formulation. The following contributions are made in this thesis: 1. The first project presents a methodology for reduction of Partial Element Equivalent Circuit (PEEC) models. PEEC method is widely used in electromagnetic compatibility and signal integrity problems in both the time and frequency domains. The PEEC model with retardation has been applied to 3-D analysis but often result in large and dense matrices, which are computationally expensive to solve. In this thesis, a new moment matching technique based on Multi-order Arnoldi is described to model PEEC networks with retardation. 2. The second project deals with developing an efficient model order reduction algorithm for simulating large interconnect networks with nonlinear elements. The proposed methodology is based on a multidimensional subspace method and uses constraint equations to link the nonlinear elements and biasing sources to the reduced order model. This approach significantly improves the simulation time of distributed nonlinear systems, since additional ports are not required to link the nonlinear elements to the reduced order model, yielding appreciable savings in the size of the reduced order model and computational time. 3. A parameterized reduction technique for nonlinear systems is presented. The proposed method uses multidimensional subspace and variational analysis to capture the variances of design parameters and approximates the weakly nonlinear functions as a Taylor series. An SVD approach is presented to address the efficiency of reduced order model. The proposed methodology significantly improves the simulation time of weakly nonlinear systems since the size of the reduced system is smaller than the original system and a new reduced model is not required each time a design parameter is changed

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

The Partial Elements Equivalent Circuit Method: The State Of The Art

This year marks about half a century since the birth of the technique known as the partial element equivalent circuit modeling approach. This method was initially conceived to model the behavior of interconnect-type problems for computer-integrated circuits. An important industrial requirement was the computation of general inductances in integrated circuits and packages. Since then, the advances in methods and applications made it suitable for modeling a large class of electromagnetic problems, especially in the electromagnetic compatibility (EMC)/signal and power integrity (SI/PI) areas. The purpose of this article is to present an overview of all aspects of the method, from its beginning to the present day, with special attention to the developments that have made it suitable for EMC/SI/PI problems

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

A fast-initializing digital equalizer with on-line tracking for data communications

A theory is developed for a digital equalizer for use in reducing intersymbol interference (ISI) on high speed data communications channels. The equalizer is initialized with a single isolated transmitter pulse, provided the signal-to-noise ratio (SNR) is not unusually low, then switches to a decision directed, on-line mode of operation that allows tracking of channel variations. Conditions for optimal tap-gain settings are obtained first for a transversal equalizer structure by using a mean squared error (MSE) criterion, a first order gradient algorithm to determine the adjustable equalizer tap-gains, and a sequence of isolated initializing pulses. Since the rate of tap-gain convergence depends on the eigenvalues of a channel output correlation matrix, convergence can be improved by making a linear transformation on to obtain a new correlation matrix