Magnetic Circuits Analogy and Energy Storage Concept
Dr. Dr. Rania Rania Swief Swief
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Magnetic Circuits
=B . a
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where, B= µ H
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R= l/ µ a
where, R is the reluctance in At/Wb
and H= NI/ lc
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= NI/R
Substituting 2 &3 in 1
= µ a NI/ lc
Dr. Dr. Rania Rania Swief Swief
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Analogy Between Electrical and Magnetic Circuit
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Example 1
Draw the equivalent magnetic circuit of the shown figure?
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Example 2
Calculate I to establish an air gap flux of 0.6T.
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From Fig
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Magnet and Coil
When a magnet is moved into a coil of wire, changing the magnetic field and magnetic flux through the coil, a voltage will be generated in the coil according to Faraday’s law.
The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. •
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Faraday's Law
Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.
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Lenz's Law
“Opposing the original flux change” means that if the flux reduced another current will be produced to keep the flux constant and vice versa
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Hysteresis loop A hysteresis loop shows the relationship between the induced magnetic flux density (B) and the magnetizing force (H). It is often referred to as the B-H loop. A ferromagnetic material that has never been previously magnetized or has been thoroughly demagnetized will follow the dashed line as H is increased.
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From the hysteresis loop, a number of primary magnetic properties of a material can be determined. Retentivity - A measure of the residual flux density corresponding to the saturation induction of a magnetic material. In other words, it is a material's ability to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. (The value of B at point b on the hysteresis curve.) Residual Magnetism or Residual Flux - the magnetic flux density that remains in a material when the magnetizing force is zero. Note that residual magnetism and retentivity are the same when the material has been magnetized to the saturation point. However, the level of residual magnetism may be lower than the retentivity value when the magnetizing force did not reach the saturation level. Coercive Force - The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetic flux return to zero. (The value of H at point c on the hysteresis curve.) Permeability, m - A property of a material that describes the ease with which a magnetic flux is established in the component. Reluctance - Is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.
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Eddy current If the source is ac, this will induces ac voltage, which will produce a current to flow in the core. This current is called eddy current. The energy dissipated due to eddy current are proportional to the size of the paths through the core. This type of energy is the form of heat dissipation because of the resistivity of the material .
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If mmf is ac , then the B-H curve will be symmetrical loop. The area within this loop is proportional to energy loss per cycle. This energy is called hysteresis loss. Both hysteresis losses and eddy losses can be summarized in iron losses or core losses term. To reduce the energy losses, the core must be constructed from thin laminations. An insulated oxide or resin is used, so the current paths for eddy currents are limited to small areas.
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Stacking Factor
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Fringing Effect Fringing results from flux lines appearing along the sides and edges of magnetic members separated by air
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Energy Storage
For a magnetic medium with no losses and constant permeability.
The air gap has linear magnetic properties, so the energy stored in the air gap can be given by:
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where, Magnetomotive force is called “mmf” is equal NI in (At), ampere turn as a unit.
where, is the flux linkage which is equal to the total flux assuming no losses.
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Inductance “L”
The definition for the inductance is the flux linkage per current. The inductance is measured by Henry. L= /I = N /I =N(NI/R)/I =N2 / R
L is a function of the geometry and permeability. So, the energy storage in an inductance with linear magnetic properties.
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Self inductance
It is the inductance of a coil is linked by its own flux
L = N /I
In a case of two coupled coils. The inductance is calculated assuming i2 is equal to zero.
L11 = N11 /I1 = N1(1+ 21) /I1
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L22 = N22 /I2 = N2(2+ 12) /I2
where, 2 and 1 are the leakage fluxes.
Mutual inductance
It is the inductance of a coil is linked by a current produced from another source.
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Let’s consider.
Similarly.
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Let’s consider M as the geometrical mean of L12 and L21.
K1
In general, L12 and L21. are almost equal to M the geometrical mean
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Energy Storage in a Coupled Coil
W=½ 1 i1 + ½ 2 i2
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1 = N11+N121 2= N22+N112 Substituting 1 and 2 in “1” .
Where,
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