Abstract
Abstract The complex initial permeability (CIP) as a function of frequency is one of the main properties of ferrites. This characteristic (CIP) is measured experimentally, therefore there can be found noisy, doubtful or incomplete parts of the spectrum. Thus there is a need for a method of evaluation of quality of CIP. In this article for evaluation of the quality of experimental CIP spectra of polycrystalline ferrite materials the KKR (Kramers-Kronig relations) are used. In order to apply KKR to experimentally measured data (i.e. data with finite limits) the method of transforming these integral relations into summation relations with finite limits is developed and described. This method can be used only for CIP given over the wide frequency rage, so that the imaginary part of CIP is fully presented. Using KKR with the help of CIP spectra model (based on the effects coming from polycrystal grain sizes and defects distribution) partly removes aforementioned limit. Thus with the help of the model we can also make CIP spectra reconstruction (in cases when CIP is noisy or incomplete) and CIP spectra decomposition.
Highlights
The research of magnetic components, used in power electronics, remains topical nowadays due to extensive use of electronics in everyday life
The analysis shows that complex initial permeability (CIP) data is precise and reliable; the data within the noisy area of the CIP was precised with the help of Kramers-Kronig relations (KKR)
This example proves the hypothesis that KKR can be used for spectra decomposition at least in the cases when domain wall (DW) and natural spin resonance (NSR) resonances can be identified
Summary
The research of magnetic components, used in power electronics, remains topical nowadays due to extensive use of electronics in everyday life. If we can repeat our own measurements again, the spectra taken for analysis from different other author’s publications should be analyzed as they are, due to inability of performing measurements of original samples This can lead to different interpretations of results. The KKR do not provide any physical nature analysis, but are used in the cases, when there is a need for mathematical evaluation of a complex function Such cases can differ: in electric circuit theory – dispersion relations connect gain frequency dependence and phase; the impedance data over limited frequency domain can be evaluated with KKR [14], [15]; refraction of light and absorption in dispersing medium in optics [16], even application of KKR to S-parameters measured by vector network analyzer [17], etc. In this paper the Kramers-Kronig relations will be used in order to evaluate the quality of the experimental CIP and precise measured CIP data
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