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Multirate partial differential algebraic equations for simulating radio frequency signals

Published online by Cambridge University Press:  01 December 2007

ROLAND PULCH ,
MICHAEL GÜNTHER  and
STEPHANIE KNORR
ROLAND PULCH
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstr. 20, D-42119 Wuppertal, Germany E-mail: pulch@math.uni-wuppertal.de, guenther@math.uni-wuppertal.de, knorr@math.uni-wuppertal.de
MICHAEL GÜNTHER
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstr. 20, D-42119 Wuppertal, Germany E-mail: pulch@math.uni-wuppertal.de, guenther@math.uni-wuppertal.de, knorr@math.uni-wuppertal.de
STEPHANIE KNORR
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstr. 20, D-42119 Wuppertal, Germany E-mail: pulch@math.uni-wuppertal.de, guenther@math.uni-wuppertal.de, knorr@math.uni-wuppertal.de
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Abstract

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and frequency may change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. We outline the theory of this multivariate approach with respect to the simulation of amplitude as well as frequency modulated signals. Furthermore, a survey of numerical methods for solving the arising problems of MPDAEs is given.

Type
A Survey in Mathematics for Industry
Information
European Journal of Applied Mathematics , Volume 18 , Issue 6 , December 2007 , pp. 709 - 743
Copyright
Copyright © Cambridge University Press 2007

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