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Time domain reflectometry of glass beads/magnetite mixtures: A time and frequency domain study
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9.This relation can be obtained by the following trivial algebra. Given and for the SF theorem, it follows and . Since for , in the frequency domain one has .
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14.A partial knowledge of the frequency dependence is accessible. Indeed, from the electrodynamics equations one obtains where the first contribution is due to the frequency dependent dielectric constant and the second one to the zero frequency conductivity . The measurements of show a weak dependence in the range 100 kHz–1 MHz, suggesting a nearly constant value of and a weak contribution of . Since no absorption is expected between the kilohertz and the gigahertz for the investigated materials, the extrapolation of the data at 1 MHz can be exploited for performing the empirical checks we propose.
15.This value holds for the specific material we consider and must be readjusted for samples of different structure or composition.
16.The value at 0% is not shown because it was very poorly determined.
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