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

Fast methods for full-wave electromagnetic simulations of integrated circuit package modules

Fast methods for the electromagnetic simulation of integrated circuit (IC) package modules through model order reduction are demonstrated. The 3D integration of multiple functional IC chip/package modules on a single platform gives rise to geometrically complex structures with strong electromagnetic phenomena. This motivates our work on a fast full-wave solution for the analysis of such modules, thus contributing to the reduction in design cycle time without loss of accuracy. Traditionally, fast design approaches consider only approximate electromagnetic effects, giving rise to lumped-circuit models, and therefore may fail to accurately capture the signal integrity, power integrity, and electromagnetic interference effects. As part of this research, a second order frequency domain full-wave susceptance element equivalent circuit (SEEC) model will be extracted from a given structural layout. The model so obtained is suitably reduced using model order reduction techniques. As part of this effort, algorithms are developed to produce stable and passive reduced models of the original system, enabling fast frequency sweep analysis. Two distinct projection-based second order model reduction approaches will be considered: 1) matching moments, and 2) matching Laguerre coefficients, of the original system's transfer function. Further, the selection of multiple frequency shifts in these schemes to produce a globally representative model is also studied. Use of a second level preconditioned Krylov subspace process allows for a memory-efficient way to address large size problems.Ph.D.Committee Chair: Swaminathan Madhavan; Committee Member: Papapolymerou John; Committee Member: Chatterjee Abhijit; Committee Member: Peterson Andrew; Committee Member: Sitaraman Sures

Novel acceleration approaches of accurate and efficient modeling of high speed interconnects in layered media

Accurate modeling of interconnect structures is an important issue in modern high frequency circuit and chip design; such as the accurate computation of the frequency dependent internal impedance of interconnect structures, like wires and conducting strips, and the accurate and efficient electromagnetic (EM) modeling for shielded microstrip structures, especially in multilayered medium. In the first part of this dissertation, a rigorous volume integral equation (VIE) is developed for the current distributions over two-dimensional conducting cylinders. For very low frequencies, it can be reduced to the widely-used quasi-static approximation. The different VIEs, surface integral equation (SIE), and partial differential equation (PDE) with Dirichlet boundary condition method are used to calculate the current distributions. The VIE with quasi-static approximation for good conductor is not accurate enough for the current distributions as there is a constant ratio between the results calculated from the quasi-static VIE and SIE. Two more leading terms from the Hankel function have been added into the integral kernel to solve this problem. We also calculate the internal impedance by using the different VIEs and the PDE with Dirichlet boundary condition method. The different results between VIE and PDE methods are due to the different boundary conditions. In the second part of this dissertation, the novel acceleration approaches for spectral domain approach (SDA) over single layer substrate and for spectral domain immitance approach (SDIA) over multilayered substrates have been developed using one of the most promising extrapolation method--the Levin\u27s transformation. It avoids the leading term extraction of the Green\u27s functions and the Bessel\u27s functions (basis functions) by recasting the summation kernel to a suitable form which can be applied in the Levin\u27s transformation. The extrapolation delay has been introduced to successfully apply the Levin\u27s transformation. Accurate results have been obtained for the propagation constant by only using twenty to thirty terms. The final accuracy could be further improved if only the first leading term added with the Levin\u27s transformation. The new techniques match with or are even better than other acceleration techniques with high order leading term extraction. The two-dimensional PMCHWT formulation was developed from internal and external equivalent problems, along with the spatial and spectral domain dyadic Green\u27s functions to deal with the arbitrary cross section and finite conductivity of multiple metal lines over multilayered substrates. The pulse and triangular basis were chosen to be applied in the Galerkin method. The matrix elements were calculated from spatial domain integration in internal equivalent problem, while in external equivalent problem we need to transfer the spatial domain integration into spectral domain summation

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

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

High-Performance Computing for the Electromagnetic Modeling and Simulation of Interconnects

The electromagnetic modeling of packages and interconnects plays a very important role in the design of high-speed digital circuits, and is most efficiently performed by using computer-aided design algorithms. In recent years, packaging has become a critical area in the design of high-speed communication systems and fast computers, and the importance of the software support for their development has increased accordingly. Throughout this project, our efforts have focused on the development of modeling and simulation techniques and algorithms that permit the fast computation of the electrical parameters of interconnects and the efficient simulation of their electrical performance

Signal and power integrity co-simulation using the multi-layer finite difference method

Mixed signal system-on-package (SoP) technology is a key enabler for increasing functional integration, especially in mobile and wireless systems. Due to the presence of multiple dissimilar modules, each having unique power supply requirements, the design of the power distribution network (PDN) becomes critical. Typically, this PDN is designed as alternating layers of power and ground planes with signal interconnects routed in between or on top of the planes. The goal for the simulation of multi-layer power/ground planes, is the following: Given a stack-up and other geometrical information, it is required to find the network parameters (S/Y/Z) between port locations. Commercial packages have extremely complicated stack-ups, and the trend to increasing integration at the package level only points to increasing complexity. It is computationally intractable to solve these problems using these existing methods. The approach proposed in this thesis for obtaining the response of the PDN is the multi-layer finite difference method (M-FDM). A surface mesh / finite difference based approach is developed, which leads to a system matrix that is sparse and banded, and can be solved efficiently. The contributions of this research are the following: 1. The development of a PDN modeler for multi-layer packages and boards called the the multi-layer finite difference method. 2. The enhancement of M-FDM using multi-port connection networks to include the effect of fringe fields and gap coupling. 3. An adaptive triangular mesh based scheme called the multi-layer finite element method (MFEM) to address the limitations of M-FDM 4. The use of modal decomposition for the co-simulation of signal nets with the PDN. 5. The use of a robust GA-based optimizer for the selection and placement of decoupling capacitors in multi-layer geometries. 6. Implementation of these methods in a tool called MSDT 1.Ph.D.Committee Chair: Madhavan Swaminathan; Committee Member: Andrew F. Peterson; Committee Member: David C. Keezer; Committee Member: Saibal Mukhopadyay; Committee Member: Suresh Sitarama

Geometry-Aware Methodology for Coupling Mechanism Analysis and Radiation Mechanism Analysis

Due to the wide-band spectrum of digital signals, a variety of noise generators, including microprocessors, liquid crystal displays, digital microphones, high-speed traces, and double-data-rate memory modules, are found in consumer electronics products. Noise generated by digital circuits can couple to the antennas and degrade their sensitivity. Additionally, it also couples to metallic housings or heatsinks and produces a significant amount of emission. In this research, methodologies are presented to analyze the coupling and radiation mechanism in electronic devices. To investigate the coupling between the distributive geometries in the radio frequency interference (RFI) problem, a mesh-dependent partition-based coupling mechanism analysis method is provided based on the retarded partial element equivalent circuit (rPEEC) model. The proposed method can quantify the capacitive and inductive coupling between the layout partitions and offers a clear physical understanding of the coupling study. The dipole moment is a popular equivalent noise source for digital circuits. The characteristic mode theory (CMT) is used as a systematic method to study the interaction between the equivalent noise source and the metallic housings. An analytic modal-based equation is used to predict the emissions. Mitigation methodologies, such as component placement and grounding post design, are also discussed based on the modal analysis results. The transfer function method is commonly used for RFI problem analysis and mitigation. In this work, using the CMT, a modal-based analysis is provided to calculate the transfer function between the aggressor and the antenna port. The interference can be mitigated by component placement and changes in the antenna designs without compromising the antenna performance --Abstract, p. i