the Hysteresis loop
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Hysteresis = when a system's current state depends on its history (present and past states) of the system.
E.g. A magnet may have 1+ possible magnetic moment in a magnetic field, depending how its field changed prior. 1 component of the moment's plots often form a loop or hysteresis curve, of a variable's different values depending on another variable's direction change, a history dependence that's the memory basis in a hard disk drive and remanence retaining Earth's magnetic field magnitude past records.
All ferromagnetic materials show the hysteresis phenomena, and in deformation of rubber bands and shape-memory alloys and other natural phenomena. In natural systems, it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.
As a magnetic dipoles change direction, the core heats up from the friction of the molecules. Hysteresis losses are a function of the volume of the core, the frequency, and the maximum flux density
Magnetic hysteresis is a phenomenon of when a ferromagnetic material's magnetic flux density (B) lags behind the magnetizing field strength (H). Such "lagging" is seen as a loop in a graph of B vs. H, called the hysteresis loop--a ferromagnetic material's property to retain some magnetism even after the external magnetic field leaves, a key characteristic in memory devices like hard drives and audio tapes.
Hysteresis loop
Hysteresis loop
A hysteresis loop/B-H relationship
[2] A hysteresis loop tells alot about a material’s magnetic properties, the relationship between the induced magnetic flux density (B) and the magnetizing force (H), the B-H loop.
Right image is
an example of the hysteresis loop:
The loop is created by measuring a ferromagnetic material's magnetic flux, which if has never been magnetized before or is throughoutly demagnetized will follow the line as "H" rises.
The line shows higher amount of current used gives a stronger magnetic field in "B+." Point "a" has almost all magnetic domains aligned and an additional rise in the magneticizing force gives little magnetic flux rise.
The material reached the magnetic saturation point. As H reduces to 0, the curve moves from "a" to "b", where some magnetic flux stays in the material regardless the magnetizing force is 0-- the point of retentivity, which tells the material's remanence/residual magnetism level.
retentivity: a substance's ability to retain/resist magnetization, often measured as the magnetic field's strength staying in a sample after a inducing field left
Some magnetic domains stay aligned and some don't.
to align: stay in a straight line
As magnetizing force reverses, the curve moves to point "c", where flux reduces to 0--curve's point of coercivity (reverse magnetizing force flips enough of the domains for the material's net flux is 0). Coercive force/The material's coercivity is the force needed to remove the material's residual magnetism.
From the hysteresis loop, a material's primary magnetic properties are found:
Retentivity is a residual flux density measure corresponding to saturation induction of a magnetic material--it's a material's ability to retain a residual magnetic field amount as the magnetizing force removes after saturating. (Value of B at point "b" on hystersis curve).
Residual magnetism or residual flux is the magnetic flux density staying in a material if the material magnetizes to saturation point. But the residual magnetism level maybe under the retentivity value if as the magnetizing force didn't reach saturation level.
Coercive force
Permeability (μ) is a material's property depicting the ease a magnetic flux establishes in a component.
Reluctance is the opposition a ferromagnetic material shows to a magnetic field's establishment and is analogous to an electrical circuit's resistance.
Types
Types
[3] There are 2 hysteresis types:
Rate-dependent hysteresis has a lag between input and output. We can take the example of a sinusoidal input X(t) resulting in a sinusoidal output Y(t), there is a phase lag φ:
Rate-independent hysteresis is in systems with a past persistent memory staying even after transients leave.
Hysteresis loss
Hysteresis loss
Hysteresis losses is when a transformer core is directly proportional to an hysteresis loop's area. The smaller a used magnetomotive force excursions on the core, smaller area of the resulting loop and so does resulting losses.
So hysteresis losses are reduced via core material off less hysteresis loop area. Silicon and steel for the transformer manufacturing core often have less hysteresis loop area.
E.g. 1#
A slice through a core.
Flux lines at right angles
The field expands.
As the field expands, lines of flux cut the core
A voltage induces.
The voltage is effectively short circuited leading to high currents.
These are known as Eddy or Foucault currents
P = I²R
B-H Relationship in vacuums
B-H Relationship in vacuums
In a vacuum, the relationship between B and H is given by: B = μ₀ H
μ₀ = vacuum/air's permeability = 4π x 10⁻⁷ wb/(A-t/m), it's a material’s ability to support a magnetic field’s formation in itself.
In vacuum, B-H relationship is linear.
B-H Relationship in magnetic materials
B-H Relationship in magnetic materials
[2.1] In magnetic materials, the relationship between B and H is: B = μ₀ μR H
μR = material’s relative permeability
μR varies via flux density so "B = μ₀ μR H" has little practical value. Curves derived from experimental data are used instead.
the B-H magnetization curve
A sheet steel's magnetic density core is 1.69 T if the magnetic intensity is 2600 A-t/m.
At the curve's pink part, magnetic density rises fast via a current rise.
Power transformers operate here (safe mode region).
Effectively the max field density is under 1.5 T.
This red part is the “knee”, where the magnetic density rise reduces.
Here, even big current rises makes little magnetic density rise. The current goes
Ampère's Law
Ampère's Law
Ampère's Law (or Magnetomotive Force, MMF equation) says a magnetic field's circulation around a closed loop is proportional to the total electric current going through a loop.
It builds a bond between electric currents and the magnetic fields they make.
Devices operations depend on magnetic density. Via ferro-magnetic materials an rise in coil current rises the flux intensity in the core, quantified in the relationship H = NI/l
H = magnetic field intensity (Amp-turns/meter)--measures how strongly a magnetic field is made per unit length of a core.
N = coil's number of turns (unitless)
I = current through the coil (amperes)
l = magnetic core's mean path length (meters)
Steinmetz equation
Steinmetz equation
The Steinmetz equation (Ph = ȠB1.6max f*V ) calculates the power loss due to a magnetic material's hysteresis or a similar empirical model:
Ƞ = Hysteresis constant (1.5 to 2.5) in J/m³
B max = max flux density in wb/m²
f = frequency
V = core’s volume
Ke = eddy current constant
t = laminations thicknesses
[4] Hysteresis and eddy currents are both energy losses in magnetic materials, but occur due to different mechanisms.
Both energy losses are part of iron losses made in a core due to an alternating magnetic field.
Hysteresis losses are proportional to frequency. Eddy current losses vary as frequency square.
Ƞ = hysteresis constant (1.5 to 2.5) in J/m³
Bmax: max flux density in wb/m²
f = frequency
V = Volume of the Core
Ke = eddy current constant
t = laminations thicknesses
Related pages
Related pages
References
References
[1] Wikipedia
[1.1] Hysteresis
[1.2] Eddy current
[1.3] Steinmetz's equation
[1.4] Ampère's circuital law
[1.5] Saturation (magnetic)
[1.7] Coercivity
[1.7]
[1.7]
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[Q1] Flashcards
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