The Use of Kramers-Kronig Relations for Verification of Quality of Ferrite Magnetic Spectra

Nikolajs Ponomarenko; Tatjana Solovjova; Juris Grizans

doi:10.1515/ecce-2015-0009

The Use of Kramers-Kronig Relations for Verification of Quality of Ferrite Magnetic Spectra

Authors

Nikolajs Ponomarenko Scientific assistant, Riga Technical University
Tatjana Solovjova Researcher, Riga Technical University
Juris Grizans Scientific assistant, Riga Technical University

DOI:

https://doi.org/10.1515/ecce-2015-0009

Keywords:

Mathematical model, Mathematical analysis, Permeability, Magnetic properties, Ferrites

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.

References

J. Jankovskis, “Complex permeability of ferrites correlated with their microstructure,” Advances in Sc. & Techn., vol. 45, pp. 2560–2565, 2006. http://dx.doi.org/10.4028/www.scientific.net/AST.45.2560

J. Jankovskis, “Relations analogous to Snoek’s one, for domain wall processes,” J. Magn Magn. Mat., vol. 304, pp. e492–e494, 2006. http://dx.doi.org/10.1016/j.jmmm.2006.02.133

S. K. Kurtz, F. M. A. Carpay, “Microstructure and normal grain growth in metals and ceramics. Pt.1.,” J. Appl. Phys., vol. 51, no. 11, pp. 5725–5744, 1980. http://dx.doi.org/10.1063/1.327580

R. L. Kronig, “On the Theory of Dispersion of X-Rays,” J. Opt. Soc. Amer., vol. 12, pp. 547–557, 1926. http://dx.doi.org/10.1364/JOSA.12.000547

D. W. Lee, S. X. Wang, Y. J. Tang, J. I. Hong, A. E. Berkowitz, “Permeability of Fine Magnetic Particles: Measurements, Calibration, and Pitfalls,” IEEE Trans. Magn., vol. 42, no. 10, 2006. http://dx.doi.org/10.1109/TMAG.2006.878872

S. Yoshida, K. Kondo, T. Kubodera, “Suppression of GHz Noise Emitted From a Four-Layered PWB With Ferrite-Plated Inner Ground Layer,” IEEE Trans. Magn., vol. 44, no. 11, 2008. http://dx.doi.org/10.1109/TMAG.2008.2001531

J. Slama, P. Shiroky, M. Shoka, et. al., “Frequency analysis of nickel based magnetic dielectrics,” J. Electr. Eng., vol. 60, no. 1, pp. 39–42, 2009.

J. Jankovskis, N. Ponomarenko, P. Narica, “An Investigation on High Frequency Permeability of Polycrystalline Ferrites,” in Proc. of the 8th Int. Sci. and Pract. Conf., Rezekne, Latvia, 20–22 June, 2011. pp. 194–201.

H. A. Kramers, “Atti del Congresso Internationale del Fisici,” Como, vol. 2, p. 545, 1927.

I. N. Bronshtein, K. A. Semendjaev, Spravochnik po matematike. Moscow, 1957.

R. Islam, Md O. Rahman, M. A. Hakim, D. K. Saha, Saiduzzaman, S. Noor, M. Al-Mamun, “Effect of Sintering temperature on Structural and Magnetic Properties of Ni0.55Zn0.45Fe2O4 Ferrites,” Materials Sciences and Applications, vol. 3, pp. 326–331, 2012. http://dx.doi.org/10.4236/msa.2012.35048

J. McCutcheon, “FFDMs Promise Optimized Wireless Power Charging,” Electronic Design, 2011, Available: http://electronicdesign.com/power/ffdms-promise-optimized-wireless-power-charging

J. Jankovskis, N. Ponomarenko, “Complex permeability of ferrites as intrinsic and extrinsic properties,” J. Chem. Chem. Eng., vol. 8, pp. 85–91, 2014.

J. Matthew Esteban, M. Orazem, “On the application of the Kramers-Kronig Relations to evaluate the consistency of electromechanical impedance data,” J. Electrochem. Soc., vol. 138, no. 1, pp. 67–76, January 1991. http://dx.doi.org/10.1149/1.2085580

D. M. Bastidas, E. Cano, J. A. Lopez-Caballero, J. L. Polo, J. M. Bastidas, “Application of Kramers-Kronig relationships for titanium impedance data validation in a Ringer’s solution,” Rev. Metal., pp. 304–311, 2004. http://dx.doi.org/10.3989/revmetalm.2004.v40.i4.278

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, E. M. Vartiainen, “Kramers-Kronig relations in optical materials research,” in Springer Series in Optical Sciences, Springer-Verlag Berlin Heidelberg, 2005.

J. Lucas, E. Geron, T. Ditchi, S. Hole, “Practical use of the Kramers-Kronig relations at microwave frequencies. Application to photonic like lines and left handed materials,” PIERS online, vol. 7, no. 4, pp. 387–393, 2011. http://dx.doi.org/10.1007/b138913

A. Cotton-Clay, “Complex Analysis,” in Mathematics 113. Analysis I: Complex Function Theory, Harvard University, Spring 2013.

L. M. Pjatigorskij, “Dispersionnie sootnoshenija,” Teoreticheskie issledovanija v oblasti fiziki. Trudi metrologicheskih institutov SSSR, vol. 102 (162), pp. 149–166.

J. Jankovskis, personal communication.