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Analytic Solution
Anisotropic Material
Differential Equation
Energy Loss
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Hysteresis and Phase Transitions
Applications of a theory of ferromagnetic hysteresis
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Mathematical theory and calculations of magnetic hysteresis curves
Mathematical theory and calculations of magnetic hysteresis curves,10.1109/20.92354,IEEE Transactions on Magnetics,M. L. Hodgdon
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Mathematical theory and calculations of magnetic hysteresis curves
(
Citations: 30
)
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M. L. Hodgdon
The differential equation, par. deltaH/par. deltat = ..cap alpha..chemically bondpar. deltaB/par. deltatchemically bond(f(B)  H) + par. deltaB/par. deltatg(B, par. deltaB/par. deltat), in which the constant ..cap alpha.. and the material functions f and g are suitably restricted, forms a theory of rateindependent and ratedependent hysteresis in ferrites, ferromagnetic materials, magnetic thin films, and permanent magnetic materials. The theory provides mathematical expressions for the initial magnetization curve, the anhysteretic curve, the major loop, the symmetric and asymmetric minor loops, and the
energy loss
associated with their traversal. Functional forms for f and g that can be scaled to measured values of the closure point, the remanence, the coercivity and, for rateindependent applications, the nonlinear changes in the loop area and
energy loss
that accompany increases in the rates par. deltaB/par. deltat and par. deltaH/par. deltat, are discussed. By allowing the material parameters to depend on angle, the variations in loop shape and coercive point with angle observed in uniaxially anisotropic materials are described. Sample calculations are presented for representative materials. 4 refs., 5 figs.
Journal:
IEEE Transactions on Magnetics  IEEE TRANS MAGN
, vol. 24, no. 6, pp. 31203122, 1988
DOI:
10.1109/20.92354
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Citation Context
(15)
...Here, the analysis is extended to other hysteretic models, such as Hodgdon [
6
], Jiles–Atherton, and its dynamic variants [7]–[9], and complemented by a comparison of the SNR and signal amplification (SA) characteristics for integral, differential, and algebraic...
...where is equal to 1 if is increasing in time and 1i f is decreasing; and are piecewise smooth material functions defined as if , if , if , and if , if , where , , , , , and are some material parameters (rateindependent parameters) [
6
]...
M. Dimian
,
et al.
Comparison of NoiseInduced Resonance Characteristics for Different Mo...
...Some models are developed mathematically [15], [
16
], and many of them, such as the Preisach [17], [18], the Jiles‐Atherton [19], and the energetic model [20], are derived from physical consideration...
Yu Zhang
,
et al.
A Novel Hysteresis Core Loss Model for Magnetic Laminations
...The wellknown nonlinear relation B = H can be implemented using several algorithms [7], [8], [9], [
10
], [11], [12]...
Jaromir Macak
.
Nonlinear transformer simulation for realtime digital audio signal pr...
...Another mathematical approach that has been applied to minor loops is Hodgdon’s differential equation model [
13
]...
Robert G. Harrison
.
Physical Theory of Ferromagnetic FirstOrder Return Curves
...In first category, mathematical models can be found [
1
], which ignore the physics of material behavior, and second category presents models based on physical considerations...
Matej Toman
,
et al.
Parameter Identification of the Jiles–Atherton Hysteresis Model Using ...
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Citations
(30)
Comparison of NoiseInduced Resonance Characteristics for Different Models of Hysteresis
M. Dimian
,
P. Andrei
,
O. Manu
,
V. Popa
Journal:
IEEE Transactions on Magnetics  IEEE TRANS MAGN
, vol. 47, no. 10, pp. 38253828, 2011
A Novel Hysteresis Core Loss Model for Magnetic Laminations
Yu Zhang
,
Ming C. Cheng
,
Pragasen Pillay
Journal:
IEEE Transactions on Energy Conversion  IEEE TRANS ENERGY CONVERS
, vol. 26, no. 4, pp. 993999, 2011
Nonlinear transformer simulation for realtime digital audio signal processing
Jaromir Macak
Published in 2011.
Magnetic Characteristics and Excess Eddy Current Losses
(
Citations: 1
)
Yu Zhang
,
M.C. Cheng
,
P. Pillay
Published in 2009.
Physical Theory of Ferromagnetic FirstOrder Return Curves
Robert G. Harrison
Journal:
IEEE Transactions on Magnetics  IEEE TRANS MAGN
, vol. 45, no. 4, pp. 19221939, 2009