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# Magnetic Circuits

Transformers

MAGNETIC CIRCUITS

A magnetic circuit is a path for magnetic flux, just as an electric circuit provides a path for the flow of electric current. Transformers, electric machines, and numerous other electromechanical devices utilize magnetic circuits. Magnetic induction or magnetic flux density, B, is defined by the force equation

F = B l I        (Formula 1)

where F (N) is the force experienced by a straight conductor oflength t(m) which carries a current i (A) and is oriented at right angles to a uniform magnetic field of flux density B (T). In other words, if a conductor is 1 meter long, carries 1 ampere of current, and experiences 1 newton force when located at right angles to parallel magnetic flux lines, then the magnetic flux density is 1 tesla. Actually, the magnetic induction is a vectar, B, of magnitude B and tangential to the flux lines. If B is uniform over a surface of area A and is everywhere perpendicular to the surface, magnetic flux, Φ, is determined by (Formula2)

The unit of magnetic flux is the weber (Wb), and (2) shows that

1 T = 1 Wb/m2.

The source of magnetic flux is either a permanent magnet or an electric current. To measure the
effectiveness of electric current in producing a magnetic field (or flux), the concept of magnetomotive force (mmf),  F, defined as

F = NI       (Formula 3)

is introduced where I  is the current flowing in an N-turn coil. The unit of F is the ampere turn (At). Schematically, a magnetic circuit with an mmf and magnetic flux is shown in below.

The core material of a magnetic circuit (constituting a transformer or an electric machine) is gen­erally ferromagnetic, and the variation of B with H (magnetic field intensity measured in units of A/m or At/m) is depicted by asaturation curve, as shown in Fig. 2. For region II, where the slope of the curve is nearly constant, we may write

B = μH         (Formula 4)

where μ, (H/m) is defined as the permeability of the material.   For free space (or air), μ = μo = 4 л  x 10-7 H/m.
Figure 2
Magnetic circuits obey the analog of Ohm´s law; the complete analogy between magnetic and dc resistive circuits is displayed in Table 13-1 ,where t is the length and A is the cross-sectional area of the path for the current in the electric circuit, or for the flux in the magnetic circuit. By the analogy, the laws of resistances in series or parallel also hold for reluctances.

 DC Resistive Circuit Magnetic Circuit current, I flux,Φ voltage, V mmf,  F conductivity, σ permeability,μ Ohm´s law, I = V / R Φ = F / R resistance, R =l / σ A reluctance, R = l /μ A conductance, G = 1/ R permeance, P = 1 / R Table 1
The dijferences between a dc resistive circuit and a magnetic circuit are:
(1)  there is an I2R-loss in a resistance but no Φ2R-loss in a reluctance;
(2) magnetic fluxes take leakage paths, as Φlin Fig. 2, whereas electric currents (flowing through resistances) do not;
(3) Magnetic circuits are non-linear through the B-H characteristic of Fig. 2;
(4) in magnetic circuits with air gaps we encounter fringing (Fig. 2) of flux lines, but we do not have fringing of currents in electric circuits. Fringing increases with the length of the air gap, and increases the effective cross-sectional area of the air gap.
Keywords : Magnetic, Induction, Transformer, Transformation, Electrical, Electronic
Writer : delon  |
16 Mar 2006 Thr
|  10.937 Views
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