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Advantages of Dual Hyperbolic Tangent Function Over Single Hyperbolic Tangent Function in Description of Hysteresis Loops


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DOI: https://doi.org/10.15866/iree.v11i5.8662

Abstract


If the mathematical description of the magnetic hysteresis loop branches should be simple, easy to use and should credibly describe the waveform magnetic hysteresis loop with a minimum number of parameters, then it inevitably leads to the description of magnetic hysteresis loop branches with a hyperbolic tangent function. This paper presents the advantages in description of magnetic hysteresis loop branches with a hyperbolic tangent function over other functions. The advantages in description of magnetic hysteresis loop branches with dual hyperbolic tangent function versus description with a single hyperbolic tangent function when the magnetic hysteresis loop has a very pronounced saturation region are provided. Also, this paper presents numerical difficulties in describing of magnetic hysteresis loop branches with a hyperbolic tangent function. Using soft magnetic material, as an example, a numerical procedure for determining parameters in description of magnetic hysteresis loop branches with a single and two hyperbolic tangent functions is shown. The numerical results are analyzed and discussed.
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Keywords


Magnetic Hysteresis; Hyperbolic Tangent Function; Dual Hyperbolic Tangent Function

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References


Juha Pyrhonen, Tapani Jokinen, Valeria Hrabovcova, Design of Rotating Electrical Machines, 2 edition , John Wiley & Sons, Ltd., 2013, ISBN: 978-1118581575
http://dx.doi.org/10.1002/9781118701591

Alex Van den Bossche, Vencislav Cekov Valchev, Inductors and Transformers for Power Electronics, 1 edition, CRC Press, 2005, ISBN: 978-1574446791
http://dx.doi.org/10.1201/9781420027280

John R. Brauer, Magnetic Actuators and Sensors, 2 edition, Wiley-IEEE Press, 2014, ISBN: 978-1118505250

Isaak D. Mayergoyz, Mathematical Models of Hysteresis and their Applications, Academic Press, 2003, ISBN 0-12-480873-5

Helmut Kronmüller, Stuart Parkin, Handbook of Magnetism and Advanced Magnetic Materials, Wiley-Interscience, 2007, ISBN: 0470022175
http://dx.doi.org/10.1002/9780470022184

K. H. J. Buschow, Handbook of Magnetic Materials, Volume 8, Elsevier, 1995, ISBN: 978-0-444-81974-1

Edward Della Torre, Magnetic Hysteresis, Wiley-IEEE Press, 1 edition, 2000, ISBN: 0-7803-6041-9
http://dx.doi.org/10.1109/9780470545195

E. P. Wohlfarth, Handbook of Magnetic Materials, North-Holland Publishing Company, 1980, ISBN: 978-0-444-85312-7

John W. Harris, Horst Stocker, Handbook of Mathematics and Computational Science, 1998, Springer – Verlag, New York, Inc. ISBN: 0-387-94746-0

F. N. Fritsch, R. E. Carlson, Monotone Piecewise Cubic Interpolation, Journal on Numerical Analysis, SIAM, Vol. 17, No. 2, April 1980
http://dx.doi.org/10.1137/0717021

István Mészáros, Complex Magnetic Characterisation of Iron-silicon Transformer Sheets, Journal of Electrical Engineering, Vol. 57. NO 8/S, 2006, pp. 151-154

István Mészáros, Magnetization curve modelling of soft magnetic alloys, Journal of Physics: Conference Series, Vol. 268 (2011), NO 1, pp. 1-6
http://dx.doi.org/10.1088/1742-6596/268/1/012020

J.Takacs, Gy. Kovacs, L. K. Varga, The Static Characteristic Loop and the External Demagnetizing Factor, Materials Sciences and Applications, 2012, 3, pp. 684-689
http://dx.doi.org/10.4236/msa.2012.310100

Krzysztof Chwastek, Higher order reversal curves in some hysteresis models, Archives of Electrical Engineering, Vol. 61(4),2012, pp. 455-470
http://dx.doi.org/10.2478/v10171-012-0036-9

Virtual Institute of Applied Science (VIAS), Free introductory textbook on the physics of capacitors, coils, and transformers, url: http://www.vias.org/about.html (accessed 9.4.2015.)

Leonardo Štrac, Modeling of Electromagnetic Properties of Steel for Calculation of Stray Losses in Power Transformers, Ph.D. dissertation, University of Zagreb, Faculty of Electrical Engineering and Computing (FER), Zagreb, 2010

Mathcad, url: http://www.ptc.com (accessed 9.4.2015.)

Matlab, url: http://www.mathworks.com (accessed 9.4.2015.)

Mathematica, url:http://www.wolfram.com (accessed 9.4.2015.)

Visio2007, url:http://office.microsoft.com (accessed 9.4.2015.)


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