Page 635 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 621
where (t) is the source voltage applied to the primary winding, N is the number of turns
1
1
of the coil, and Φ is the magnetic flux. Assuming no loss in the magnetic flux, the induced
B
voltage in the secondary winding is
dΦ B
(t) =−N (8.82)
2 2
dt
N 2
(t) = (t) (8.83)
2
1
N 1
Notice that when N > N , the transformer increases the voltage (step-up transformer), and
2 1
when N < N , it reduces the voltage (step-down transformer, Figure 8.11). Notice that a
2
1
transformer works on the AC voltage. The DC component of the voltage in the primary
winding does not cause any change in the magnetic field, hence does not contribute to the
voltage induced in the secondary winding. Therefore, a transformer is sometimes used to
isolate (or block) the DC component of a source voltage in signal processing applications.
When N = N , there is no AC voltage level change between primary and secondary
2
1
windings, and such a transformer is called the isolation transformer. The main purpose of
an isolation transformer is to “isolate” the two devices on the primary side and secondary
side from each other so that there are no physical ground loops between the two sides.
Example Consider the electromagnetic circuit shown in Figure 8.12. The core of the
coil winding is made of a magnetically conductive material with a permeability coefficient
of . The cross-sectional area, the length of the core material, and the total number of turns
c
of the solenoid are A , l , N, respectively. Let the air gap distance be l . The cross-sectional
g
c c
area at the air gap is A . Determine the effective reluctance and inductance of the circuit.
g
The reluctance of the magnetically permeable core and air gap add in series like
electrical resistance.
R = R + R (8.84)
c g
l c l g
= + (8.85)
⋅ A c ⋅ A g
c
0
Notice that if ≫ , then R ≈ R .
g
0
c
A c

l
R g g
N i . A
l g g
N i .
A g

(a) (b)
FIGURE 8.12: (a) An electromagnetic circuit example: coil wound over a core which has an air
gap. (b) Magnetic circuit model.