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Article

Edita Kolarova and Lubomir Brancik

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Abstract

Purpose

The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise.

Design/methodology/approach

The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus.

Findings

Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations.

Practical implications/implications

The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated.

Originality/value

The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 36 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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Article

Lubomír Brančík

The purpose of this paper is to present the development and comparison of selected time‐domain and Laplace‐domain methods for the simulation of waves propagating along…

Abstract

Purpose

The purpose of this paper is to present the development and comparison of selected time‐domain and Laplace‐domain methods for the simulation of waves propagating along multiconductor transmission lines (MTLs), both uniform and nonuniform, and sensitivities with respect to distributed and lumped parameters of MTL systems.

Design/methodology/approach

A methodology is based on discrete, semidiscrete and continuous MTL models formulated and solved both in the time and Laplace domains, latter combined with a numerical inverse Laplace transform (NILT).

Findings

The most accurate method is that based on the MTL Laplace‐domain continuous model, processed via the MTL chain matrix and connected with an NILT. This method concurrently shows minimal RAM requirements, and in case of uniform MTLs, it runs fastest. For nonuniform MTLs, however, the implicit Wendroff formula is fastest, as long as the RAM is available.

Research limitations/implications

The research is limited to linear MTLs only and the methods suppose terminating circuits based on their generalized Thévenin equivalents. They can be, however, generalized for more complex systems via more sophisticated boundary conditions treatment. The time‐domain methods have further potential to be generalized towards nonlinear MTLs.

Practical implications

The methods considered can contribute to solving signal integrity issues in high‐speed electronic systems, the Matlab routines developed can serve in education process as well.

Originality/value

The implicit Wendroff formula has been adapted to enable simulation of voltage and/or current distributions and their sensitivities along the nonuniform MTLs' wires. Besides, semidiscrete and continuous nonuniform MTL models have been elaborated to enable sensitivities determination, both in the time and Laplace domains, latter connected with the NILT technique based on fast Fourier transform/inverse fast Fourier transform and quotient‐difference algorithms.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

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