Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Abstract—This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time–space adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index Terms—Electromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I

High-Performance Passive Macromodeling Algorithms for Parallel Computing Platforms

This paper presents a comprehensive strategy for fast generation of passive macromodels of linear devices and interconnects on parallel computing hardware. Starting from a raw characterization of the structure in terms of frequency-domain tabulated scattering responses, we perform a rational curve fitting and a postprocessing passivity enforcement. Both algorithms are parallelized and cast in a form that is suitable for deployment on shared-memory multicore platforms. Particular emphasis is placed on the passivity characterization step, which is performed using two complementary strategies. The first uses an iterative restarted and deflated rational Arnoldi process to extract the imaginary Hamiltonian eigenvalues associated with the model. The second is based on an accuracy-controlled adaptive sampling. Various parallelization strategies are discussed for both schemes, with particular care on load balancing between different computing threads and memory occupation. The resulting parallel macromodeling flow is demonstrated on a number of medium- and large-scale structures, showing good scalability up to 16 computational core

On the Generation of Large Passive Macromodels for Complex Interconnect Structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed technique

Broadband whole package FDTD simulation

Whole package analysis is becoming more and more important with the rapid expansion of high frequency electronics. The motivation of this thesis is to find and implement a new method for broadband whole package simulation. 3-dimension (3-D) whole package Finite Difference Time Domain (FDTD) simulation result was first reported in detail in this thesis. The FDTD method is a widely used full-wave time-domain simulation method used in the design and analysis for electromagnetic (EM) systems, such as antennas, wave propagating, and microwave circuits. Absorbing boundary condition (ABC), such as the perfect matched layer (PML) method, makes it possible to accurately analyze an EM structure involving complicated wave propagation in three-dimensional domain. Instead of running simulation at each frequency, time-domain solution gives complete frequencydomain response including coupling and dispersion effects. Chapter2 introduces the principle of FDTD and two important boundary condition methods. It also discusses the nonuniform grid numerical error, and gives the FDTD simulation and theoretical result. Flip chip package is one of the most important package types. Chapter 3 presents a wide band approach for characterizing multiple flip chips interconnects by the FDTD method. Detailed analysis for electrical performance for frequencies up to 40 GHz has been performed with variations of interconnect bumps (ball cross section and via cross section). Flip chips of three sizes are studied using FDTD method in detail. The relationship between reflection loss, via pad length, ball crosssection and via cross section is tabulated for future packaging design. Based on the simulation results, some design approaches are proposed for packaging structure operating at near 40 GHz. FDTD whole package simulation method is introduced at the beginning of Chapter 4, followed by discussion how to implement this method to specific packages. The packages used to host circuit in chapter 4 are microstrip line and fiip chip interconnects. The embedded circuits are ideal transmission line and an HP amplifier. Transient effects are observed when an amplifier is hosted in a package. Most of the simulations are processed under three-dimensional environment; twodimensional simulation is used for reference standard. All these results were first reported by the author of this thesis and his collaborators

Modeling Noise Coupling Between Package and PCB Power/Ground Planes with an Efficient 2-D FDTD/Lumped Element Method

An efficient numerical approach based on the 2-D finite-difference time-domain (FDTD) method is proposed to model the power/ground plane noise or simultaneously switching noise (SSN), including the interconnect effect between the package and the print circuit board (PCB). The space between the power and ground planes on the package and PCB are meshed with 2-D cells. The equivalent R-L-C circuits of the via and the solder balls connecting the package and PCB can be incorporated into a 2-D Yee cell based on a novel integral formulation in the time domain. An efficient recursive updating algorithm is proposed to fit the lumped networks into the Yee equations. A test sample of a ball grid array (BGA) package mounted on a PCB was fabricated. The power/ground noise coupling behavior was measured and compared with the simulation. The proposed method significantly reduces the computing time compared with other full-wave numerical approaches

Efficient full-wave modeling of radiative near-field interactions in semi-anechoic conditions

In this paper, a full-wave method to efficiently compute the electromagnetic interaction between two devices placed in semi-anechoic conditions is proposed. The aim of this research is the accurate and efficient reproduction of radiated immunity and emission tests in simulation. The employed technique relies on a single simulation (or measurement) of the radiation pattern of each device and allows an arbitrary relative position between the devices. The resulting procedure is practical, has a low computational cost, and shows good agreement with reference solutions

Master of Science

thesisAdvances in silicon photonics are enabling hybrid integration of optoelectronic circuits alongside current complementary metal-oxide-semiconductor (CMOS) technologies. To fully exploit the capability of this integration, it is important to explore the effects of thermal gradients on optoelectronic devices. The sensitivity of optical components to temperature variation gives rise to design issues in silicon on insulator (SOI) optoelectronic technology. The thermo-electric effect becomes problematic with the integration of hybrid optoelectronic systems, where heat is generated from electrical components. Through the thermo-optic effect, the optical signals are in turn affected and compensation is necessary. To improve the capability of optical SOI designs, optical-wave-simulation models and the characteristic thermal operating environment need to be integrated to ensure proper operation. In order to exploit the potential for compensation by virtue of resynthesis, temperature characterization on a system level is required. Thermal characterization within the flow of physical design automation tools for hybrid optoelectronic technology enables device resynthesis and validation at a system level. Additionally, thermally-aware routing and placement would be possible. A simplified abstraction will help in the active design process, within the contemporary computer-aided design (CAD) flow when designing optoelectronic features. This thesis investigates an abstraction model to characterize the effect of a temperature gradient on optoelectronic circuit operation. To make the approach scalable, reduced order computations are desired that effectively model the effect of temperature on an optoelectronic layout; this is achieved using an electrical analogy to heat flow. Given an optoelectronic circuit, using a thermal resistance network to abstract thermal flow, we compute the temperature distribution throughout the layout. Subsequently, we show how this thermal distribution across the optoelectronic system layout can be integrated within optoelectronic device- and system-level analysis tools

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