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

Influence of the line characterization on the transient analysis of nonlinearly loaded lossy transmission lines

The analysis of nonlinearly terminated lossy transmission lines is addressed in this paper with a modified version of a method belonging to the class of mixed techniques, which characterize the line in the frequency domain and solve the nonlinear problem in the time domain via a convolution operation. This formulation is based on voltage wave variables defined in the load sections. The physical meaning of such quantities helps to explain the transient scattering process in the line and allows us to discover the importance (so far often overlooked) of the reference impedance used to define the scattering parameters. The complexity of the transient impulse responses, the efficiency of the algorithms, and the precision of the results are shown to be substantially conditioned by the choice of the reference impedance. The optimum value of the reference impedance depends on the amount of line losses. We show that a low-loss line can be effectively described if its characteristic impedance or the characteristic impedance of the associated LC line is chosen as the reference impedance. Based on the physical interpretation of our formulation, we are able to validate the numerical results, and to demonstrate that, despite claimed differences or improvements, the formulations of several mixed methods are fundamentally equivalen

Compressed Passive Macromodeling

This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model order. For such structures, standard approaches based on rational approximation via vector fitting and passivity enforcement via model perturbation may fail because of excessive computational requirements, both in terms of memory size and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated singular value decomposition. Then we formulate a compressed rational fitting and passivity enforcement framework which is able to obtain speedup factors up to 2 and 3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed techniqu

Implementation of interconnect simulation tools in spice

Accurate computer simulation of high speed digital computer circuits and communication circuits requires a multimode approach to simulate both the devices and the interconnects between devices. Classical circuit analysis algorithms (lumped parameter) are needed for circuit devices and the network formed by the interconnected devices. The interconnects, however, have to be modeled as transmission lines which incorporate electromagnetic field analysis. An approach to writing a multimode simulator is to take an existing software package which performs either lumped parameter analysis or field analysis and add the missing type of analysis routines to the package. In this work a traditionally lumped parameter simulator, SPICE, is modified so that it will perform lossy transmission line analysis using a different model approach. Modifying SPICE3E2 or any other large software package is not a trivial task. An understanding of the programming conventions used, simulation software, and simulation algorithms is required. This thesis was written to clarify the procedure for installing a device into SPICE3E2. The installation of three devices is documented and the installations of the first two provide a foundation for installation of the lossy line which is the third device. The details of discussions are specific to SPICE, but the concepts will be helpful when performing installations into other circuit analysis packages