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

Thermal Noise Compliant Synthesis of Linear Lumped Macromodels

This paper addresses the synthesis of equivalent circuits from black box state-space macromodels, as produced by model order reduction or rational curve fitting schemes. The emphasis is here on thermal noise compliance, intended as the guarantee that the produced netlists can be safely used in standard circuit solvers to perform thermal noise analysis, in addition to usual DC, AC, and transient simulations. Due to the fact that SNR is a key figure of merit in nearly all signal processing analog circuits, noise analysis is mandatory in design and verification of most analog and RF/millimeter-wave electronic applications. However, common macromodel synthesis approaches rely on components that do not (and cannot) have an associated thermal noise model, such as controlled sources or negative circuit elements. Therefore, macromodel-based noise analyses are generally not possible with currently available approaches. We propose a circuit realization derived from the classical resistance extraction synthesis, with suitable modifications for enhancing macromodel sparsity and efficiency. The resulting equivalent netlist, which is compatible with any standard circuit solver, is shown to produce exact noise characteristics, even if its elements are derived through a mathematical procedure, totally unrelated to the actual topology of the physical system under modeling. The procedure is validated by several examples

Coherent photonic crossbar as a universal linear operator

Linear optics aim at realizing any real- and/or complex-valued matrix operator via optical elements, addressing a broad field of applications in the areas of quantum photonics, microwave photonics and optical neural networks. The transfer of linear operators into photonic experimental layouts typically relies on Singular Value Decomposition (SVD) techniques combining meshes of cascaded 2x2 Mach Zehnder Interferometers (MZIs), with the main challenges being the precision in the experimental representation of the targeted matrix, referred to as fidelity, and the overall insertion loss. We demonstrate a novel interferometric coherent photonic crossbar architecture (Xbar) that demarcates from state-of-the-art SVD implementations and can realize any linear operator, supporting full restoration of the loss-induced fidelity. Its novel interferometric design allows for the direct mapping of each matrix element to a single, designated Xbar node, bringing down the number of programming steps to only one. We present the theoretical foundations of the Xbar, proving that its insertion losses scale linearly with the node losses as opposed to the exponential scaling witnessed by the SVD counterparts. This leads to a matrix design with significantly lower overall insertion losses compared to SVD-based schemes when utilizing state-of-the-art silicon photonic fabrication metrics, allowing for alternative node technologies with lower energy consumption and higher operational speed credentials to be employed. Finally, we validate that our Xbar architecture is the first linear operator that supports fidelity restoration, outperforming SVD schemes in loss- and phase-error fidelity performance and forming a significantly more robust layout to loss and phase deviations

Longitudinal Partitioning Waveform Relaxation Methods For The Analysis of Transmission Line Circuits

Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits. The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic suboptimal numerical solution of the min-max problem is presented and a procedure to construct its objective function is suggested. Numerical examples illustrate the parallelizability and good scaling of the WR algorithm and point out to the limitation of resistive coupling. In the second WR algorithm, resistances from the previous insertion are replaced with dissipative impedances to address the slow convergence of standard resistive coupling of the first algorithm for low-loss highly reactive circuits. The pertinence and feasibility of impedance coupling are demonstrated and the properties of the subsequent WR method are studied. A new coupling strategy proposes judicious approximations of the optimal convergence conditions for faster speed of convergence. The proposed strategy avoids the difficult problem of optimisation and uses coarse macromodeling of the transmission line to construct approximations with delay under circuit form. Numerical examples confirm a superior speed of convergence which leads to further runtime saving. Finally, new results concerning the nilpotent WR algorithm are presented for chains of circuits when dissipative coupling is used. It is shown that optimal local convergence is necessary to achieve the optimal WR algorithm. However, the converse is not correct: the WR algorithm with optimal local convergences factors can be nilpotent yet not optimal or even be non-nilpotent at all. The second analysis concerns resistive coupling. It is demonstrated that WR always converges for chains circuits. More precisely, it is shown that WR will converge independently of the length of the chain when this late is made of identical symmetric circuits

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

Switched-capacitor networks for image processing : analysis, synthesis, response bounding, and implementation

Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.Includes bibliographical references (p. 279-284).by Mark N. Seidel.Sc.D