Publication detail

Two-Dimensional Laplace Transformation in Linear Circuit Simulation

BRANČÍK, L.

Original Title

Two-Dimensional Laplace Transformation in Linear Circuit Simulation

English Title

Two-Dimensional Laplace Transformation in Linear Circuit Simulation

Type

conference paper

Language

en

Original Abstract

In the paper an unconventional method of a simulation of linear lumped–distributed circuits based on a Laplace transformation in two variables is discussed. Distributed parts are formed by uniform multiconductor transmission lines (MTL). Essentially two partial Laplace transformations are performed, with respect to the time t and coordinate x, to transform MTLs‘ partial differential equations into the algebraic ones. Considering further boundary conditions a two-dimensional transform in the (q,s)-domain is derived. Finally a method of the numerical inversion of 2D Laplace transforms is used to obtain the solution in the (x,t)-domain. Unlike previous works where generalized Thevenin/Norton equivalents have been used here modified nodal admittance equation method (MNA) is applied to incorporate the boundary conditions into a solution. By this arbitrarily complex circuits can be taken into account. Using universal scientific language Matlab voltage and/or current wave propagations along MTLs’ wires can effectively be stated and visualized.

English abstract

In the paper an unconventional method of a simulation of linear lumped–distributed circuits based on a Laplace transformation in two variables is discussed. Distributed parts are formed by uniform multiconductor transmission lines (MTL). Essentially two partial Laplace transformations are performed, with respect to the time t and coordinate x, to transform MTLs‘ partial differential equations into the algebraic ones. Considering further boundary conditions a two-dimensional transform in the (q,s)-domain is derived. Finally a method of the numerical inversion of 2D Laplace transforms is used to obtain the solution in the (x,t)-domain. Unlike previous works where generalized Thevenin/Norton equivalents have been used here modified nodal admittance equation method (MNA) is applied to incorporate the boundary conditions into a solution. By this arbitrarily complex circuits can be taken into account. Using universal scientific language Matlab voltage and/or current wave propagations along MTLs’ wires can effectively be stated and visualized.

Keywords

Two-dimensional Laplace transformation, numerical inversion, distributed circuit, Matlab

RIV year

2003

Released

06.07.2003

Location

Warsaw

ISBN

83-916444-1-3

Book

Proceedings of ISTET´03, XII. International Symposium on Theoretical Electrical Engineering

Edition

Vol. 1

Edition number

1.

Pages from

101

Pages to

104

Pages count

4

BibTex

``````
@inproceedings{BUT9374,
author="Lubomír {Brančík}",
title="Two-Dimensional Laplace Transformation in Linear Circuit Simulation",
annote="In the paper an unconventional method of a simulation of linear lumped–distributed circuits based on a Laplace transformation in two variables is discussed. Distributed parts are formed by uniform multiconductor transmission lines (MTL). Essentially two partial Laplace transformations are performed, with respect to the time t and coordinate x, to transform MTLs‘ partial differential equations into the algebraic ones. Considering further boundary conditions a two-dimensional transform in the (q,s)-domain is derived. Finally a method of the numerical inversion of 2D Laplace transforms is used to obtain the solution in the (x,t)-domain. Unlike previous works where generalized Thevenin/Norton equivalents have been used here modified nodal admittance equation method (MNA)  is applied to incorporate the boundary conditions into a solution. By this arbitrarily complex circuits can be taken into account. Using universal scientific language Matlab  voltage and/or current wave propagations along MTLs’ wires can effectively be stated and visualized.",
booktitle="Proceedings of ISTET´03, XII. International Symposium on Theoretical Electrical Engineering",
chapter="9374",
edition="Vol. 1",
year="2003",
month="july",
pages="101",
type="conference paper"
}``````