Abstract
Abstract. 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.
Highlights
In electrical engineering the dispersion phenomenon is wellknown as a frequency-dependent variation of the phase velocity of electromagnetic waves due to specific material properties
Dispersion is closely related to the causality principle meaning that a cause can never happen after the corresponding effect
Kronig (1926) proved that the dispersion in a medium is a direct consequence of the causality principle
Summary
In electrical engineering the dispersion phenomenon is wellknown as a frequency-dependent variation of the phase velocity of electromagnetic waves due to specific material properties. The KramersKronig (KK) transforms generally relate the real and the imaginary parts of a complex quantity describing a causal system. There are some constraints for any complex quantity to satisfy the KK-transforms such as stability and linearity (Esteban and Orazem, 1991; Macdonald and Urquidi-Macdonald, 1990, 1985). Macdonald and Urquidi-Macdonald (1990) suggested that these relations can be employed to resolve the complex impedance data of any electrochemical system They proved that the electrical equivalent circuit of any electrochemical impedance should follow the KK-transforms provided that it satisfies the aforementioned constraints
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