Hardware Reference

In-Depth Information

Example-1: Magnetic circuit of an inductor

An electromagnetic device is shown in Figure 4.5. This is an inductor formed

by a winding and a magnetic core made of steel. There is an airgap in the core.

The core is of uniform cross section and the number of turns in the winding

is N. Input current I into the winding, and the magnetic
fi
eldisthusexcited

in the core as shown in Figure 4.5. To simplify the analysis, it is assumed

that the permeability of the steel is in
fi
nite, and the magnetic
fi
eld distributed

evenly in the core and airgap, and there is no leakage
fi
eld in the airgap.

Figure 4.5: Magnetic circuit of an inductor

Using Ampere's law, the relationship between the magnetic
fl
ux and current

can be described by the following close loop line integration

I

H.dl = NI,

(4.9)

l

where N is the number of turns in the winding, and I is the current going

through the winding.

Use the middle line of the core as the integration line l. Since the direction

of the
fl
ux intensity H isthesameasthatofdl, the integration can be simpli
fi
ed

as

H
c
L
c
+ H
g
g = NI,

(4.10)

where,

H
c

:
fl
ux intensity in the core,

H
g

:
fl
ux intensity in the airgap,

l
c

:

length of the core, and

g

:

length of the airgap.