A magnetic circuit is a circuit generally made out of ferromagnetic material with through which a flow of magnetic field circulates

The magnetic field is generally created either by the rollings up enclosing the magnetic circuit and crossed by currents, or by Aimant S contained in the magnetic circuit.

When several electrical circuits are wound around the same magnetic circuit, they constitute magnetically coupled Circuits.

Constitution, manufacture

It consists of an assembly of ferromagnetic material parts. It can include/understand a Entrefer : small space of air in the circuit.

This air-gap can be:

• structural: it is the case in the revolving machines where the rotor is separated from the stator by an air-gap which one wishes smallest possible;
• intentional: allows to avoid the saturation of the magnetic circuit and confers a greater linearity on the Inductance thus created.

Magnetic circuit subjected to a magnetic field independent of time

If the magnetic field is constant during time, the magnetic losses: losses by loss and Eddy current by Hystérésis are non-existent. The magnetic circuit thus often consists of massive soft iron or cast steel: materials and most economic manufacturing processes.

Magnetic circuit subjected to a periodic magnetic field of low frequency

It is necessary in this case to limit the magnetic losses.

• the losses by hysteresis are limited by the use of materials to narrow cycle .
• the losses by eddy currents are limited by a flaky preparation magnetic circuit: To replace a massive part, one carries out a sheet stacking isolated the ones from the others. The purpose of the insulation is to prevent the circulation of currents from one plate to another.

Magnetic circuit subjected to a periodic magnetic field high frequency

The losses by eddy currents increase according to the square of the frequency. The magnetic circuits used in high frequency must be realized using insulating ferromagnetic materials.

• the Ferrite S are mixed Iron III oxides and other metals M divalent. (M can be also iron. In this case ferrite obtained is called magnetite). The most used for the constitution of magnetic circuits are ferrites containing zinc (Zn) and/or of manganese (Mn).
• the materials nanocristallins are agglomerates of crystals whose size is about ten nanometers, drowned in an amorphous phase. They consist of iron, other metals (copper, niobium) and metalloids (carbon, silicon, boron). Their coercive excitations being very weak, about A/m, they present a very narrow hysteresis loop.

Analogy of Hopkinson

Principles

This analogy consists in making a parallel between the electrical circuits and the magnetic circuits.

Reluctance of a magnetic circuit

Reluctance of a homogeneous magnetic circuit

For a homogeneous magnetic circuit, i.e. made up of only one material and homogeneous section, there exists a relation making it possible to calculate its reluctance according to the material which constitutes it and of its dimensions:

$\backslash \; mathcal\; \{R\}\; =\; \backslash \; frac\; \{1\}\; \{\backslash \; driven\}\; \backslash \; cdot\; \backslash \; frac\; L\; S\; \backslash ,$ in H ^-1

• $\backslash \; driven\; \backslash ,$ being the magnetic Permeability in kg·m.A^-2·s^-2,

• $l\; \backslash ,$la length in Meter S,
• $S\; \backslash ,$ the section in m².

Equivalent reluctance of an air-gap

The reluctance of an air-gap low thickness is given by

$\backslash \; mathcal\; \{R\}\; =\; \backslash \; frac\; \{E\}\; \{\backslash \; mu\_0\; \backslash \; cdot\; S\}\; \backslash ,$, with:

• $e\; \backslash ,$ thickness of the air-gap,
• $\backslash \; mu\_0\; \backslash ,$ permeability of the vacuum
• $S\; \backslash ,$ section of the air-gap

If the thickness of the air-gap is large, there are more possible to consider only the lines of magnetic field remain perpendicular to the air-gap. One must then take account of the blooming of the magnetic field i.e. to consider that the section S is larger than that of the metal parts on both sides of the air-gap.

Reluctance of a heterogeneous circuit

The laws of association of the reluctances make it possible to calculate that of a magnetic circuit of form complex or composed of materials to the different magnetic characteristics. One breaks up this circuit into section homogeneous, i.e. of the same section and made up of same material.

• Association in series: When two homogeneous sections having respectively for reluctance $\backslash \; mathcal\; \{R\}\; \_1$ and $\backslash \; mathcal\; \{R\}\; \_2$ follow one another, the reluctance of the unit is $\backslash \; mathcal\; \{R\}\; \_\; \{eq.\; series\}\; =\; \backslash \; mathcal\; \{R\}\; \_1\; +\; \backslash \; mathcal\; \{R\}\; \_2$

• Association in parallel: When two homogeneous sections having respectively for reluctance $\backslash \; mathcal\; \{R\}\; \_1$ and $\backslash \; mathcal\; \{R\}\; \_2$ are placed side by side, the reluctance of the unit is $\backslash \; mathcal\; \{R\}\; \_\; \{eq.\; //\}$ such as $\backslash \; frac\; \{1\}\; \{\backslash \; mathcal\; \{R\}\; \_\; \{eq.\; //\}\}\; =\; \backslash \; frac\; \{1\}\; \{\backslash \; mathcal\; \{R\}\; \_1\}\; +\; \backslash \; frac\; \{1\}\; \{\backslash \; mathcal\; \{R\}\; \_2\}$, is still $\backslash \; mathcal\; \{R\}\; \_\; \{eq.\; //\}\; =\; \backslash \; frac\; \{\backslash \; mathcal\; \{R\}\; \_1.\; \backslash \; mathcal\; \{R\}\; \_2\}\; \{\backslash \; mathcal\; \{R\}\; \_1\; +\; \backslash \; mathcal\; \{R\}\; \_2\}$.

Using these laws one can calculate the reluctance of the magnetic circuit complexes in his entirety.

See too

Related articles

• Magnetism

• Electric transformer
• Reel (electricity)

External bonds

• Magnetic circuits of the machines

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