WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. By Christophe Caloz and Tatsuo Itoh.

[신간안내] Computational Electrodynamics (the finite difference time - domain method)

Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically. We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itself.

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Stability, Causality, and Passivity in Electrical Interconnect Models

Planar circuits for microwaves and lightwaves

This paper presents a strategy for the construction of parameterized linear macromodels from tabulated port responses. These macromodels are able to reproduce the input-output behavior of the structure of interest both in terms of frequency and one or more design variables such as geometry and material parameters. A highly efficient combination of rational identification and piecewise linear interpolation leads to a macromodel form which can be cast as a polytopic descriptor form. This in turns enables the construction of a numerically robust testing procedure, based on linear matrix inequalities, for the assessment of uniform model stability within any prescribed region of the parameters space. Several numerical examples are used to illustrate the theory on practical application cases.

/pdf/a-parameterized-macromodeling-strategy-with-uniform-41sexxzuyz.pdf

A Parameterized Macromodeling Strategy With Uniform Stability Test

We present a robust and efficient scheme for the generation of delay-based macromodels from frequency-domain tabulated responses. These responses can come from both simulation or direct measurement. The main algorithm is based on an iterative weighted least-squares process for the identification of delayed rational approximations. In case that pole relocation is performed during the iterations, the scheme can be interpreted as a generalization of the well-known vector fitting algorithm to delayed systems. Therefore, we denote this algorithm as delayed vector fitting (DVF). In case no pole relocation is performed, the scheme generalizes the so-called Sanathanan-Koerner iteration, calling for the denomination of delayed Sanathanan-Koerner algorithm. These techniques produce compact macromodels that are readily synthesized in SPICE-compatible equivalent circuits including delayed sources or ideal transmission line elements. These macromodels outperform classical rational macromodels in terms of simulation time. Several examples illustrate the advantages of proposed methodology.

Delay-Based Macromodeling of Long Interconnects From Frequency-Domain Terminal Responses

We present an efficient numerical technique for calculating the series impedance matrix of systems with round conductors. The method is based on a surface admittance operator in combination with the method of moments and it accurately predicts skin and proximity effects. The application to a three-phase armored cable with wire screens demonstrates a speedup by a factor of about 100 compared to a finite-elements computation. The inclusion of proximity effect, in combination with the high efficiency, makes the new method very attractive for cable modeling within Electromagnetic Transients Program-type simulation tools. Currently, these tools can only take skin effect into account.

An Equivalent Surface Current Approach for the Computation of the Series Impedance of Power Cables with Inclusion of Skin and Proximity Effects

The availability of accurate and broadband models for underground and submarine cable systems is of paramount importance for the correct prediction of electromagnetic transients in power grids. Recently, we proposed the MoM-SO method for extracting the series impedance of power cables while accounting for the skin and proximity effects in the conductors. In this paper, we extend the method to include ground return effects and to handle cables placed inside a tunnel. Numerical tests show that the proposed method is more accurate than widely used analytic formulas, and is much faster than existing proximity-aware approaches, such as finite elements. For a three-phase cable system in a tunnel, the proposed method requires only 0.3 s of CPU time per frequency point, against the 8.3 min taken by finite elements, for a speed up beyond 1000 X.

Piero Triverio

Papers

Stability, Causality, and Passivity in Electrical Interconnect Models

A Parameterized Macromodeling Strategy With Uniform Stability Test

Delay-Based Macromodeling of Long Interconnects From Frequency-Domain Terminal Responses

An Equivalent Surface Current Approach for the Computation of the Series Impedance of Power Cables with Inclusion of Skin and Proximity Effects

MoM-SO: A Complete Method for Computing the Impedance of Cable Systems Including Skin, Proximity, and Ground Return Effects