# CHAPTER 14

```CHAPTER 14
TRANSFORMER
CHAPTER OBJECTIVES
Explain mutual inductance
Describe how a transformer in constructed and
how it works
Explain how a step-up transformer works
Explain how a step-down transformer works
Discuss the effect of a resistive load across the
secondary winding
Discuss the concept of a reflected load in the
transformer
CHAPTER OBJECTIVES
Discuss impedance matching with transformers
Explain how the transformer acts as an isolation
device
Describe a practical transformer
Describe several types of transformers
THE BASIC TRANSFORMER
A basic transformer is an electrical device
constructed of two coils placed in close proximity
to each other so that there is a mutual
inductance.
One coil is called the primary winding and the
other is called the secondary winding as
indicated.
Mutual Inductance
When two coils are placed close to each other,
a changing electromagnetic field produced by
the current in one coil will cause an induced
voltage in the second coil.
When a second coil is placed vary close to the
first coil so that the changing magnetic lines of
force cut through the second coil
When two coils are magnetically coupled, they
provide electrical isolation because there is no
electrical connection between them.
Mutual Inductance
The amount of voltage induced in the second
coil as a result of the current in the first coil is
dependent on the mutual inductance, LM
The mutual inductance is established by the
inductance of each coil and by the amount of
coupling (k) between two coils
Coefficient of Coupling
Coefficient of coupling (k) between two coils is
the of the lines of force (flux) produced by coil 1
that link coil 2 to the total flux produced by coil 1
φ 1− 2
k =
φ1
A greater value of k (no unit) means that more
voltage is induced in coil 2 for a certain rate of
change of current in coil 1.
Formula for Mutual Inductance
The three factors that influence mutual
inductance are ( k, L1 and L2 ) and the
formula for mutual inductance is
LM = k
L1 L 2
THE BASIC TRANSFORMER
The winding of a transformer are formed
around the core. Three general categories
of core material are air, ferrite, and iron.
The schematic symbol for each type is
CORE MATERIALS
Air-core and ferrite-core
 Air-core and ferrite-core transformer generally
are used for high-frequency applications and
the wire is typically covered by vanish-type
coating to prevent the winding from shorting
together.
 The amount of magnetic coupling between
the primary winding and the secondary
winding is set by the type of core material and
by the relative positions of the winding
tighter the coupling, the greater the
 The
induced voltage in the secondary for a given
current in the primary
CORE MATERIALS
Iron-core
 Iron-core transformer generally are used for
audio frequency (AF) and power applications.
 A core constructed from laminate sheets of
ferromagnetic material.
 The core type has more room for insulation
and can handle higher voltages, and the shell
type can produce higher core flux.
Types of transformers
Turns Ratio
The turns ratio (n) is defined as the ratio
of the number of turns in the secondary
winding (Nsec) to the number of turns in the
primary winding (Npri)
n =
N sec
N
pri
Direction of Windings
The direction of the windings determines
the polarity of the voltage across the
secondary winding with respect to the
voltage across the primary winding
STEP-UP TRANSFORMER
The secondary voltage is greater than the
primary voltage, and the amount that the
voltage is stepped up depends on the
turns ratio.
The ratio is illustrated as :
Vsec
V pri
=
N sec
N pri
Vsec = nV pri
Primary
Secondary
STEP-DOWN TRANSFORMER
The secondary voltage is less than the
primary voltage, and the amount that the
voltage is stepped up depends on the
turns ratio which is always less than 1.
Primary
Secondary
When a load is connected to the
secondary winding of the transformer, the
power delivered to the load can never be
greater than the power delivered by the
primary winding.
For an ideal transformer Psec = Ppri
The power delivered by the primary is
Ppri = Vpri Ipri
The power delivered by the secondary is
Psec = Vsec Isec
I pri
I s ec
I s ec
= n
1
=
I pri
n
The load (RL) in the secondary of a transformer
is reflected into the primary by transformer
action.
The actual load is essentially ‘reflected’ into the
primary determined by the turns ratio.
R pri
RL
=
V pri I pri
V sec I sec
⎛ V pri
=⎜
⎜V
⎝ sec
⎞ ⎛ I sec
⎟⎜
⎟⎜ I
⎠ ⎝ pri
2
R pri
⎞ ⎛ 1 ⎞⎛ 1 ⎞ ⎛ 1 ⎞ 2
⎟ = ⎜ ⎟⎜ ⎟ = ⎜ ⎟
⎟ ⎝ n ⎠⎝ n ⎠ ⎝ n ⎠
⎠
⎛1⎞
= ⎜ ⎟ RL
⎝n⎠
SOURCE RESISTANCE
Using the concept of maximum power
transfer
Recall the maximum power transfer
theorem

When a source is connected to a load,
maximum power is delivered to the load when
the load resistance is equal to the internal
source resistance
Impedance Matching
A special type of wide-band transformer
that make the load resistance appear to
have the same value as the source
resistance is called an impedance-matching
transformer, and this technique is called
impedance matching
Impedance Matching
An antenna system has a characteristic
resistance of 75 Ω which is not equal to
the 300 Ω TV input, and thus we need a
matching transformer for matching and
maximum power will be delivered to the
input of the TV
THE TRANSFORMER AS AN
ISOLATION DEVICE
DC Isolation


When a direct current voltage is supplied to
the primary of transformer, nothing happens
in the secondary circuit.
A small transformer can be used to keep the
dc voltage on the output of an amplifier stage
from affecting the dc bias of the next amplifier
Power Line Isolation
To prevent the shock hazard, if the 220 V
or 110V line is connected to the metal
chassis of the equipment.
NONIDEAL TRANSFORMER
CHARACTERISTICS
Winding resistance

Both the primary and the secondary winding
of a practical transformer have winding
resistance.
Loss in the core

There is always some energy conversion in
the core material of a practical transformer
because of the continuous reversal of the
magnetic field due to the changing direction of
the primary current; this component of the
energy conversion is called hysteresis loss
NONIDEAL TRANSFORMER
CHARACTERISTICS
Magnetic flux leakage

Some of magnetic flux
line produced by the
primary current break
out of the core and
pass through the
surrounding air back to
the other end of the
winding
Winding capacitance
Transformer Power rating
A power transformer is typically rated in
volt-amperes (VA)
For example: 2 kVA, 500/50, 60 Hz.
The transformer rating can be helpful in
selecting the proper transformer for a
given application
Transformer efficiency
⎛ Pout
η = ⎜⎜
⎝ Pin
⎞
⎟⎟100 %
⎠
OTHER TYPE OF TRANSFORMER
Tapped Transformer
OTHER TYPE OF TRANSFORMER
Tapped Transformer
OTHER TYPE OF TRANSFORMER
Multiple-winding transformers
OTHER TYPE OF TRANSFORMER
Autotransformers
SUMMARY
A transformer generally consists of two or more coils that
are magnetically coupled on a common core.
There is mutual inductance between two magnetically
coupled coils.
When current in one coil changes, voltage is induced in
the other coil.
The primary is the winding connected to the source, and
the secondary is the secondary winding determine the
turns ratio.
The relative polarities of the primary and secondary
voltages are determined by the direction of the windings
around the core.
SUMMARY
A step-up transformer has a turns ratio greater
than 1.
A step-down transformer has a turns ratio less
than 1.
A transformer cannot increase power.
In an ideal transformer, the power from the
source (input power) is equal to the power
delivered to the load (output power)
If the voltage is stepped-up, the current is
stepped-down, and vice versa.
SUMMARY
A load connected across the secondary winding of a
transformer appears to the source as a reflected load
having a value dependent on the reciprocal of the turns
ratio squared.
An Impedance-matching transformer can match a load
resistance to an internal source resistance to achieve
maximum power transfer to the load by selection of the
proper turn ratio.
A transformer does not respond to constant dc.
Conversion of electrical energy to heat in an actual
transformer results from winding resistances, hysteresis
loss in the core, eddy currents in the core, and flux
leakage.
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