MNA stamping for transient circuit simulation using SPICE

Simulation is an essential step in the circuit design procedure, helping to verify the behavior of a designed circuit and dramatically reducing the time and effort required for debugging a given design. However, to analyze this behavior, we require an interface between the circuit design and the computer’s computational capabilities. This translation can be done in various ways depending on what aspect of the circuit is desired to be modeled (steady-state, transient, etc.). In this thesis, we explore two of these (steady-state MNA formulation and State-Space formulation) as a first step towards transient analysis

Modeling the practical performance of switched-capacitor converters and a method for automating state-space model generation

A new modeling technique and a method for automating the modeling process are introduced for analyzing complex switched-capacitor (SC) converters. The model uses conventional circuit analysis methods to derive state-space models of each switching state. Steady-state performance is derived and expressed as an equivalent resistance. Whereas previous techniques have provided either the detailed performance of a simple SC converter or the limiting performance of a complex SC converter, this new model is flexible enough to provide detailed performance for any practical converter. Nonuniform component choices, asymmetric duty cycles, and other deviations from an ideal converter can be readily included. Dynamics can also be analyzed. Iterative methods of design based on this model would require the formulation of many equations, which is time consuming if done manually. Therefore, an algorithm is introduced to automatically generate the equations required for this state-space based modeling. The state equations are generated algorithmically given a standard node incidence matrix generated from a user-defined netlist. The algorithm enables a designer to quickly iterate SC converter design solutions based on its predicted performance. The model and algorithm have been validated through simulation techniques and experimental data collected from laboratory testing --Abstract, page iii

Robust Convergence of Power Flow using Tx Stepping Method with Equivalent Circuit Formulation

Robust solving of critical large power flow cases (with 50k or greater buses) forms the backbone of planning and operation of any large connected power grid. At present, reliable convergence with applications of existing power flow tools to large power systems is contingent upon a good initial guess for the system state. To enable robust convergence for large scale systems starting with an arbitrary initial guess, we extend our equivalent circuit formulation for power flow analysis to include a novel continuation method based on transmission line (Tx) stepping. While various continuation methods have been proposed for use with the traditional PQV power flow formulation, these methods have either failed to completely solve the problem or have resulted in convergence to a low voltage solution. The proposed Tx Stepping method in this paper demonstrates robust convergence to the high voltage solution from an arbitrary initial guess. Example systems, including 75k+ bus test cases representing different loading and operating conditions for Eastern Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.Interconnection of the U.S. power grid, are solved from arbitrary initial guesses

Parameterized partial element equivalent circuit method for sensitivity analysis of multiport systems

This paper presents a new technique to perform parameterized sensitivity analyses of systems that depend on multiple design parameters, such as layout and substrate features. It uses the electromagnetic (EM) method called partial element equivalent circuit to compute state space matrices at a set of design space points. These EM matrices are interpolated as functions of the design parameters. The proposed interpolation scheme allows the computation of the derivatives of the matrices, which are needed to perform the sensitivity analysis. An extensive study of the required stability and passivity properties of the system involved in the parameterized sensitivity analysis is presented. Pertinent numerical results demonstrate the robustness, accuracy, and efficiency of the proposed methodology

Pade-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systems

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are characterized as Pade-type or even true Pade approximants of the system's transfer function, in general, these models do not preserve the form of the original higher-order system. In this paper, we present a new approach to reduced-order modeling of higher-order systems based on projections onto suitably partitioned Krylov basis matrices that are obtained by applying Krylov-subspace techniques to an equivalent first-order system. We show that the resulting reduced-order models preserve the form of the original higher-order system. While the resulting reduced-order models are no longer optimal in the Pade sense, we show that they still satisfy a Pade-type approximation property. We also introduce the notion of Hermitian higher-order linear dynamical systems, and we establish an enhanced Pade-type approximation property in the Hermitian case

Physics-based passivity-preserving parameterized model order reduction for PEEC circuit analysis

The decrease of integrated circuit feature size and the increase of operating frequencies require 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, for the analysis and design of high-speed circuits. Very large systems of equations are often produced by 3-D electromagnetic methods, and model order reduction (MOR) methods have proven to be very effective in combating such high complexity. During the circuit synthesis of large-scale digital or analog applications, it is important to predict the response of the circuit under study as a function of design parameters such as geometrical and substrate features. Traditional MOR techniques perform order reduction only with respect to frequency, and therefore the computation of a new electromagnetic model and the corresponding reduced model are needed each time a design parameter is modified, reducing the CPU efficiency. Parameterized model order reduction (PMOR) methods become necessary to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as geometrical layout or substrate characteristics. We propose a novel PMOR technique applicable to PEEC analysis which is based on a parameterization process of matrices generated by the PEEC method and the projection subspace generated by a passivity-preserving MOR method. The proposed PMOR technique guarantees overall stability and passivity of parameterized reduced order models over a user-defined range of design parameter values. Pertinent numerical examples validate the proposed PMOR approach

An intrinsic Hamiltonian formulation of the dynamics of LC-circuits

First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduce