It can be concluded from the above analysis that, for a given magnetic
circuit, the magnitude of the fl ux can be calculated using the MMF consumed
in the circuit and the reluctance of the circuit. If the MMF generated by the
winding current is fi xed, changing circuit reluctance by modifying the area of
cross section or the length of airgap or both alters the induced fl ux.
While equation 4.17 may look simple, it includes all the factors affecting
the magnetic fi eld, e.g., structure of the core, materials used, input current,
and number of turns in the winding. Using this magnetic circuit method, the
quantity of the magnetic fi eld obtained is fl ux, which is an integrated value, or
global value, of the magnetic fi eld. The fl ux density B and the fi eld intensity
H can be derived using equations 4.1, 4.3 and 4.9.
Structures of many EM systems are more complicated than the one shown
in Figure 4.5. But the magnetic circuit model which may include multiple
MMF sources and reluctances can still be used to describe these EM systems.
The reluctances may be connected in series or in parallel to form a complicated
network. Similarity between magnetic and electric circuits allows us to apply
methods used in analyzing electric circuits to the analysis of a magnetic cir-
cuit network. Non-linearity of ferromagnetic materials can also be taken into
consideration in the analysis .
It is evident from the above analysis that MMF can be linked directly to
the fl ux density in the airgap
F g =
B g .
This implies that the waveform of the MMF on the airgap has the same shape
as the airgap fl ux density. This concept can be used to simplify the analysis
of the effects of airgap fi elds in EM devices.
Example-2: Magnetic circuit of a permanent magnet motor
Let us consider the EM device shown in Figure 4.6, which is a simpli fi ed
structure of motor. The stator core and rotor are made of steel, and their per-
meabilities are assumed in fi nite. The demagnetization curve of the permanent
magnet materials is shown in Figure 4.7.
If the airgap length g is much smaller than the radius of the rotor, the
surfaces of the stator core and the rotor on the two sides of the airgap can be
A g =rlθ m ,
where, r is the average radius of the airgap, and l m is the thickness of the
motor core (Figure 4.6). Let us select the center line of the device (shown by
broken line in Figure 4.6) as the line of integration. There is no current in this
loop and the magnetic circuit is formed only by one magnet and two airgap.