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Transformers
Transformers are some of the most efficient
machines that can be built, with efficiencies
exceeding 99%. Only simple machines (levers,
inclined planes, etc.) are more efficient.
Transformers have no moving parts, making them
extremely reliable.
The electrical insulation is about the only
component of a transformer that can fail.
Transformers
Transformers
Devices comprised of two electric circuits (isolated
from each other) linked by a magnetic circuit.
When a time-varying current flows in the first
electric circuit, a time-varying magnetic flux is
established in the magnetic circuit.
When this time-varying flux links the second
electric circuit, a time-varying voltage is induced,
per Faraday’s Law.
Magnetic Circuits
Magnetic circuits are somewhat analogous to DC electric circuits.
Electrical Quantity
Magnetic Quantity
Voltage (volts)
Magnetomotive Force (ampere-turns)
Current (amperes)
Magnetic Flux (webers)
Resistance (ohms)
Reluctance (ampere-turns per weber)
V=IR
=
Magnetic Properties
Transformer steel is made of alloys very different
from structural steels (low in carbon, high in
silicon).
Each molecule of the steel core is a magnetic dipole
(think of a tiny bar magnet).
Normally, the north and south poles (magnetic
domains) are randomly aligned to give no net
magnetic effect.
But if the domains are aligned, magnetism is
achieved.
The alignment of the magnetic domains is called
magnetic flux.
Magnetic Materials
B
H
Starting from zero, gradually increase the current flowing
through a coil. This increases the magnetic field (H)
surrounding the coil. As H increases, the magnetic flux
density (B) also increases – almost linearly at first, but
eventually undergoes saturation.
Magnetic Materials
B
H
When the current is decreased, H also decreases. But B
decreases at a lesser rate than at which it increased.
There is a tendency for aligned magnetic domains to
remain aligned. When H reaches zero, the remaining B is
called the residual magnetism or residual induction.
Magnetic Materials
B
H
Further decreasing the current (becoming negative)
drives the flux density to zero. The point at where B=0
defines the coercive force of the material. A further
decrease in current leads to a negative saturation point.
Magnetic Materials
B
H
Increasing the current increases B, but in a non-linear
way. The curve passes to the right of the origin, but
intersects itself at the positive saturation point. This
closed path is known as a hysteresis loop.
Magnetic Materials
B
The area inside
the hysteresis
loop represents
the energy lost
per cycle in the
magnetic
material.
This energy loss
shows up as
heat.
H
Laminated Steel
Insulated thin steel sheets called laminations are stacked
to form a magnetic core.
The laminations reduce eddy currents.
Winding Conductor
Transformer winding conductor is usually rectangular in
cross-section, and is insulated with Kraft paper.
The conductor material can be copper or aluminum.
Copper is mechanically stronger, so is preferred for
larger transformers. Smaller transformers often use
aluminum windings to reduce cost.
Ideal Transformers
v1  N1
d
dt
v1i1  v2i2
and v2  N 2
d
dt
Vˆ2 N 2

n
Vˆ1 N1
Iˆ1 Vˆ2 N 2
 
n
ˆI
ˆ
V1 N1
2
Ideal Transformers
Example: Redraw the diagram below twice as a single
electric circuit, the first time reflected to the high-voltage
circuit, and the second time reflected to the low-voltage
circuit.
Ideal Transformers
Reflected to the high-voltage circuit:
Ideal Transformers
Reflected to the low-voltage circuit:
Real Transformers
Must account for:
• Resistance in the winding conductors
• Power (I2R) losses
• Leakage reactance
• Flux produced by one winding that does not
link the other
• Energy to magnetize core
• Alignment of magnetic domains in core steel
• Electrical losses in core
• Hysteresis and eddy currents
Real Transformers