1,720,976 research outputs found
Waveform Relaxation Time Domain Solver for Subsystem Arrays
No full textIn this paper we present a waveform relaxation approach for the transient analysis of 3-D electromagnetic problems using the partial element equivalent circuit (PEEC) method. Relying on weaker couplings among separated systems, a waveform relaxation scheme is proposed to accelerate the transient analysis of large electromagnetic problems. The results are compared with those obtained using a conventional PEEC formulation. They exhibit a significant speed-up while preserving the solution accuracy
Fast multipole and multifunction PEEC methods
No full textA key use of the Partial Element Equivalent Circuit (PEEC) method is the solution of combined electromagnetic and circuit problems as they occur in many situations such as today's integrated circuit (VLSI) systems and as components in mobile devices. The method, which has been applied to a multitude of electrical interconnect and package problems, is very flexible since it is easy to add new features to the approach. However, faster solutions are of interest since the problems to be solved are continuously increasing in size. A class of fast methods are evolving based on the faster evaluation of the matrix elements and the use of iterative or other matrix solvers of the resultant system for the frequency domain. Fast circuit matrix solvers are easier to obtain in the time domain than the frequency domain since the delay or retardation can be utilized to sparsify the circuit matrix. In this paper, we concentrate on techniques for the fast evaluation of the PEEC circuit elements for both the frequency and time domain where possible since they both are important for the solution of specific problems
Skin-Effect Loss Models for Time- and Frequency-Domain PEEC Solver
No full textA challenging and interesting issue for the solution of large electromagnetic problems is the efficient, sufficiently accurate modeling of the broadband skin-effect loss for conducting planes and 3-D shapes. The inclusion of such models in an electromagnetic (EM) solver can be very costly in compute time and memory requirements. These issues are particularly important for the class of signal, power, and noise integrity (NI) problems. In this paper, we concentrate on partial element equivalent circuit (PEEC)-type methods which are suitable for the solution of this class of problems. Progress has been made recently in the design of skin-effect models. The difficult issues are broadband frequency-domain or time-domain problems. These models are considered in this paper. We present several solution methods, and we compare results obtained with these approaches
Analytical integration of quasi-static potential integrals on nonorthogonal coplanar quadrilaterals for the PEEC method
No full textThe rapid and accurate evaluation of the partial inductances and the normalized coefficients of potential is very important for the partial element equivalent circuit method. The evaluation of these parameters is much more challenging for the case of nonorthogonal conductors. This paper proposes an integration strategy on nonorthogonal coplanar quadrilateral domains for the quasi-static Green's function and a closed form solution for the integrals is obtained. The developed formulas, suitable for a practical implementation of the method, are compared to accurate numerical quadrature routines
PEEC Modeling of Dispersive and Lossy Dielectrics
No full textIn this paper a general formulation is presented for the time-domain partial element equivalent circuit method in a general dispersive medium. The formulation is based on Debye and Lorentz models where the resulting model is passive. The incorporation of such models into a partial element equivalent circuit solver is described by both convolution techniques and equivalent circuits. The new circuit models can be applied in the frequency as well as the time domain. Numerical examples are given to validate the proposed formulation and to show that the proposed method is accurately capturing the physics of dispersive and lossy dielectrics
Physics-Based Passivity-Preserving Parameterized Model Order Reduction for PEEC Circuit Analysis
No full textPartial and Internal Inductance: Two of Clayton R. Paul's Many Passions
No full textInductance is one of the fundamental defined parameters in electromagnetics and it takes on a variety of formulations and definitions in the electromagnetic compatibility (EMC) community. The concept of inductance in its many definitions, uses, and caveats was central among Dr. Clayton R. Paul's contributions to the EMC community. In this paper, we discuss the various aspects of inductance which Dr. Paul helped to pioneer. In particular, the concepts of partial inductance and internal inductance (including skin effect) were two of his passions. This paper will both serve as a summary of Dr. Paul's work on inductance as well as show how his work helped pioneer new research in this area
Impact of partial element accuracy on PEEC model stability
No full textThis paper details the impact of partial element accuracy on quasi-static partial element equivalent circuit (PEEC) model stability in the time domain. The potential sources of inaccurate partial element values are found to be poor geometrical meshing and the use of unsuitable partial element calculation routines. The impact on PEEC model stability of erroneous partial element values, and the coefficients of potential and partial inductances, are shown as theoretical constraints and practical results. Projection meshing, which is a discretization strategy suitable for the PEEC method, is shown to improve calculated partial element values for the same number of unknowns, thus improving model stability
Reduced order modeling of delayed PEEC circuits
No full textWe propose a novel model order reduction technique that is able to accurately reduce electrically large systems with delay elements, which can be described by means of neutral delayed differential equations. It is based on an adaptive multipoint expansion and model order reduction of equivalent first order systems. The neutral delayed differential formulation is preserved in the reduced model. Pertinent numerical results validate the proposed model order reduction approach
Interpolation-Based Parameterized Model Order Reduction of Delayed Systems
No full text"\"Three-dimensional electromagnetic methods are fundamental tools for the analysis and design of high-speed systems. These methods often generate large systems of equations, and model order reduction (MOR) methods are used to reduce such a high complexity. When the geometric dimensions become electrically large or signal waveform rise times decrease, time delays must be included in the modeling. Design space optimization and exploration are usually performed during a typical design process that consequently requires repeated simulations for different design parameter values. Efficient performing of these design activities calls for parameterized model order reduction (PMOR) methods, which are able to reduce large systems of equations with respect to frequency and other design parameters of the circuit, such as layout or substrate features. We propose a novel PMOR method for neutral delayed differential systems, which is based on an efficient and reliable combination of univariate model order reduction methods, a procedure to find scaling and frequency shifting coefficients and positive interpolation schemes. The proposed scaling and frequency shifting coefficients enhance and improve the modeling capability of standard positive interpolation schemes and allow accurate modeling of highly dynamic systems with a limited amount of initial univariate models in the design space. The proposed method is able to provide parameterized reduced order models passive by construction over the design space of interest. Pertinent numerical examples validate the proposed PMOR approach.\"
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