Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity
<p>While measuring the effective permittivity of dispersive material it may be of interest to distinguish between conductivity losses (caused by free electrons) and dielectric losses (caused by bounded electrons) which both are included in the imaginary part. This usually turns out to be a...
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2018-09-01
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doaj-ba88a80ac8d24333a24d53afd0ee0afb2020-11-24T22:26:33ZdeuCopernicus PublicationsAdvances in Radio Science 1684-99651684-99732018-09-0116232810.5194/ars-16-23-2018Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex PermittivityM. Bakry0L. Klinkenbusch1Institute of Electrical Engineering and Information Technology, Kiel University, Kiel, GermanyInstitute of Electrical Engineering and Information Technology, Kiel University, Kiel, Germany<p>While measuring the effective permittivity of dispersive material it may be of interest to distinguish between conductivity losses (caused by free electrons) and dielectric losses (caused by bounded electrons) which both are included in the imaginary part. This usually turns out to be a non-trivial task unless suitable dispersion models for the dielectric and/or the conductivity properties of the material are assumed. In this paper we present a more general method based on the Kramers-Kronig transformations to separate the conductivity from the effective complex permittivity of a dispersive material. The Kramers-Kronig transforms (or KK-transforms) are unique integral relations between the real and the imaginary part of a complex quantity describing a causal system. The proposed method and the corresponding algorithm are tested by first supposing some fictitious values of the complex permittivity satisfying the KK-transforms. Then, different values of a conductivity are added leading to a change of the imaginary part of the effective permittivity while the real part remains the same. The effective permittivity (including a conductivity part) does generally not satisfy the KK-transforms. This fact will be employed to retrieve the conductivity from that effective complex permittivity. Finally the method is applied to measured values found in the literature to retrieve the conductivity from the effective permittivity of composite material.</p>https://www.adv-radio-sci.net/16/23/2018/ars-16-23-2018.pdf |
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DOAJ |
language |
deu |
format |
Article |
sources |
DOAJ |
author |
M. Bakry L. Klinkenbusch |
spellingShingle |
M. Bakry L. Klinkenbusch Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity Advances in Radio Science |
author_facet |
M. Bakry L. Klinkenbusch |
author_sort |
M. Bakry |
title |
Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity |
title_short |
Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity |
title_full |
Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity |
title_fullStr |
Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity |
title_full_unstemmed |
Using The Kramers-Kronig Transforms To Retrieve The Conductivity From The Effective Complex Permittivity |
title_sort |
using the kramers-kronig transforms to retrieve the conductivity from the effective complex permittivity |
publisher |
Copernicus Publications |
series |
Advances in Radio Science |
issn |
1684-9965 1684-9973 |
publishDate |
2018-09-01 |
description |
<p>While measuring the effective permittivity of dispersive material it may be
of interest to distinguish between conductivity losses (caused by free
electrons) and dielectric losses (caused by bounded electrons) which both are
included in the imaginary part. This usually turns out to be a non-trivial
task unless suitable dispersion models for the dielectric and/or the
conductivity properties of the material are assumed. In this paper we present
a more general method based on the Kramers-Kronig transformations to separate
the conductivity from the effective complex permittivity of a dispersive
material. The Kramers-Kronig transforms (or KK-transforms) are unique
integral relations between the real and the imaginary part of a complex
quantity describing a causal system. The proposed method and the
corresponding algorithm are tested by first supposing some fictitious values
of the complex permittivity satisfying the KK-transforms. Then, different
values of a conductivity are added leading to a change of the imaginary part
of the effective permittivity while the real part remains the same. The
effective permittivity (including a conductivity part) does generally not
satisfy the KK-transforms. This fact will be employed to retrieve the
conductivity from that effective complex permittivity. Finally the method is
applied to measured values found in the literature to retrieve the
conductivity from the effective permittivity of composite material.</p> |
url |
https://www.adv-radio-sci.net/16/23/2018/ars-16-23-2018.pdf |
work_keys_str_mv |
AT mbakry usingthekramerskronigtransformstoretrievetheconductivityfromtheeffectivecomplexpermittivity AT lklinkenbusch usingthekramerskronigtransformstoretrievetheconductivityfromtheeffectivecomplexpermittivity |
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