Hardware Reference

In-Depth Information

Taking equation 4.3 into consideration, the relationship described by equa-

tion 4.10 can be rewritten as,

B
c
L
c

µ
c

+
B
g
g

µ
0

= NI,

(4.11)

where,

B
c

:
fl
ux density in the core,

B
g

:
fl
ux density in the airgap,

µ
c

: permeability of the core, and

µ
0

: permeability of air.

Since the
fl
ux lines are continuous and the cross-section areas of the core

and the airgap are same, it can be assumed that

B
c
= B
g
.

(4.12)

The permeability of steel is very large compared to that of airgap making

the
fi
rst term in the left hand side of equation 4.11 negligible. With that

assumption, equations 4.11 and 4.12 can be combined into

B
c
= B
g
= NI
µ
0

g
.

(4.13)

This equation can also be used to de
fi
ne the
fl
ux,

φ
g
= φ
c
= B
c
A
c
= NI
µ
0
A
c

g

=
NI

g
,

(4.14)

in which, A
c
is the area of cross section of the core, and
g
is de
fi
ned as the

reluctance of the magnetic circuit,

g

µ
0
A
c
.

g
=

(4.15)

De
fi
ning the Magnetromotive force (MMF) as

F = NI,

(4.16)

the MMF consumed by the reluctance
g
can be expressed as,

F
g
= φ
g
.

(4.17)

referring to the circuit shown in Figure 4.5, as there is only one signi
fi
cant

reluctance
g
, the MMF consumed in the airgap reluctance is equal to the

MMF generated by the winding current, that is

F = F
g
.

(4.18)