Chapter 14
Transformers
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Objectives
Explain mutual inductance
Describe how a transformer is constructed and how it
works
Explain how a step-up and -down transformer works
Discuss the effect of a resistive load across the
secondary winding
Discuss impedance matching with transformers
Explain how the transformer acts as an isolation device
Describe a tapped transformer
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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 because of the mutual inductance, LM
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Coefficient of Coupling
The coefficient of coupling (k) between two coils is
the ratio of the lines of force (flux) produced by one
coil linking the second coil (φ1-2) to the total flux
φ1− 2
produced by the first coil (φ1):
k=
φ1
The coefficient of coupling depends on the physical
closeness of the coils and the type of core material on
which they are wound
The formula for mutual inductance:
LM = k√ L1L2
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The Basic Transformer
Source voltage is applied to the primary winding
The load is connected to the secondary winding
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The Basic Transformer
The core (air, ferrite or iron) provides a physical structure
for placement of windings and a magnetic path so that the
magnetic flux lines are concentrated close to the coils
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Turns Ratio
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 sec
n=
N pri
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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
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Direction of Windings
Phase dots are used to indicate polarities
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Step-Up Transformers
A transformer in which the secondary voltage is
greater than the primary voltage is called a stepup transformer
The ratio of secondary voltage (Vsec) to primary
voltage (Vpri) is equal to the ratio of the number of
turns in the secondary winding (Nsec) to the
number of turns in the primary winding (Npri)
Vsec N sec
=
=n
V pri N pri
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Step-Up Transformers
Example: The transformer has a turns ratio of 3. What is
the voltage across the secondary?
Vsec = (3/1)(120V) = 360 V
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Step-Down Transformer
A transformer in which the secondary voltage is
less than the primary voltage is called a stepdown transformer
The amount by which the voltage is stepped down
depends on the turns ratio
The turns ratio of a step-down transformer is
always less than 1
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Step-Down Transformers
Example: The transformer is part of a laboratory power
supply and has a turns ratio of 0.2. What is the
secondary voltage?
Vsec = (0.2)(120V) = 24 V
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Primary Power Equals
Load Power
For an ideal transformer, the power delivered in
the secondary equals the power in the primary
In a real transformer, some power is dissipated in
the transformer, so primary power is always
greater than secondary power
In an ideal transformer, power transfer is not
related to the turns ratio
Ppri = VpriIpri = VsecIsec = Psec
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Loading the Secondary Winding
When a load resistor is connected to the secondary
winding, there is a current through the resulting
secondary circuit because of the voltage induced
in the secondary coil
This secondary current results in a primary
current
I sec N pri
=
I pri N sec
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Loading the Secondary Winding
Example: The two transformers have loaded secondaries. If
the primary current is 100 mA in each case, what is the
current through the load?
(a) IL = (1/10)(100mA) = 10 mA
(b) IL = (2/1)(100mA) = 200 mA
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Reflected Load
This reflected load is what the primary source effectively
see, and it determines the amount of primary current
The effective resistance that the primary sees is
R pri
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⎛ N pri
= ⎜⎜
⎝ N sec
2
⎞
⎛1⎞
⎟⎟ RL = ⎜ ⎟ RL
⎝n⎠
⎠
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Reflected Load
Example: What is the reflected resistance seen by the source
Rpri = (1/4)2(100Ω) = 6.25 Ω
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Impedance Matching
When a source is connected to a load, maximum power is
delivered to the load when the load impedance is equal to
the fixed internal source impedance
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Matching Transformer
One application of transformers is in the matching of
a load resistance to a source resistance in order to
achieve maximum transfer of power
2
⎛1⎞
R pri = ⎜ ⎟ R L
⎝n⎠
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⎛1⎞
75 = ⎜ ⎟ (300 )
⎝n⎠
20
n=
300
=
75
4=2
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DC Isolation
A transformer does not pass dc, therefore a transformer
can be used to keep the dc voltage on the output of an
amplifier stage from affecting the bias of the next amplifier
The ac signal is coupled through the transformer between
amplifier stages
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Tapped Transformers
The center tap (CT) transformer is equivalent to
two secondary windings with half the voltage
across each
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Tapped Transformers
Power company step down the high voltage from the
power line to 100V/220V service for residential and
commercial customers
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Summary
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 winding connected to the
load
The number of turns in the primary and the number
of turns in the secondary determine the turns ratio
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Summary
The relative polarities of the primary and secondary
voltages are determined by the direction of the
windings around the core
A step-up transformer has a turns ratio greater than 1
A step-down transformer has a turns ratio less than 1
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
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Summary
A load 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
selecting the proper turns ratio
A typical transformer does not respond to dc
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