electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
Chapter 14 - Transformers
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Transformers
Mutual Inductance
• When two coils are placed close to each other:
1. a changing flux in one coil will cause an
induced voltage in the second coil.
• Electrical isolation – condition in which two
circuits have no common conductive path.
• Mutual inductance (LM) determines the amount of
voltage induced in the second coil based on the
amount of current in the first coil.
LM
L2
L1
k
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Transformers
Mutual Inductance
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Transformers
Mutual Inductance
LM  k L1L2
k = the coefficient of coupling (dimensionless)
L1, L2 = inductance of each coil (Henry)
• The coefficient of coupling depends on:
1. orientation of the coils to each other,
2. their proximity, and
3. if they are on a common core.
• The coefficient of coupling is a measure of how well the
coils are linked; it is a number between 0 and 1.

k

1  2
LM
 - Flux (W )
b
1
L2
L1
k
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Transformers
Example 1: Two coils are wound on a single core, and the
Coefficient of coupling is 0.3. The inductance of coil 1
is 10µH, and the inductance of coil 2 is 15µH. What is Lm?
LM  k L1L2
Example 2: Determine the coefficient of coupling when
LM = 2µH, L1 = 16µH, L2 = 4µH.
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Transformers
Basic Transformer
Transformer
1. Electrical device constructed of two or more
coils of wire (windings)
2. Electromagnetically coupled to each other
3. With a mutual inductance to transfer power from
one coil to the other coil
Schematic symbols indicate the type of core.
Air core
Ferrite core
Iron core
Small power transformer
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Transformers
Basic Transformer
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Transformers
Basic Iron Core Transformer
Core Type - Easy to insulate
Shell Type – higher core flux
thus less turns are required
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Transformers
Transformers with cylindrical-shaped cores.
Usually used for high frequency applications
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Transformers
Some common types of transformers
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Transformers
Turns ratio
Ratio of turns in the secondary winding (Nsec) to the
number of turns in the primary winding (Npri)
n
N sec
N pri
n = turns ratio
Nsec = number of secondary windings
Npri = number of primary windings
* Based on the IEEE dictionary definition for electronics power transformers.
Most transformers are not marked with turns ratio.
A transformer has 800 turns on the primary and
a turns ratio of 0.25. How many turns are on
the secondary? 200
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Transformers
Direction of windings
Determines the polarity of the voltage across the
secondary winding with respect to the voltage across the
primary.
Phase dots are sometimes used to indicate polarities.
Phase Dots
In phase
Out of phase
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Transformers
Step-up and Step-down transformers
For any 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),
V sec N sec

Vpri
Npri
 N sec 
V sec  
Vpri
 Npri 
V sec  nVpri
n = turns ratio
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Transformers
Step-up and step-down transformers
In a step-up transformer, the secondary voltage is
greater than the primary voltage and n > 1.
In a step-down transformer, the secondary voltage is
less than the primary voltage and n < 1.
What is the secondary voltage?
4:1
Vpri
120 Vrms
?30 Vrms
What is the turns ratio? 0.25
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Transformers
Isolation transformers
• A special transformer with a turns ratio of 1 is called
an isolation transformer.
• Because the turns ratio is 1, the secondary voltage is
the same as the primary voltage
•  ac is passed from one circuit to another.
Isolation
transformer
1:1
120 Vac
120 Vac
• The isolation transformer breaks the dc path between
two circuits while maintaining the ac path.
• The dc is blocked by the transformer, because magnetic
flux does not change with dc.
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Transformers
Current
• Transformers cannot increase the applied power.
• If the secondary voltage is higher than the primary
voltage, then the secondary current must be lower than
the primary current.
• If the secondary voltage is less than the primary
voltage, then the secondary current must be higher
than the primary current.
Ppri=VpriIpri
Ideally
Psec=VsecIsec
Ppri must always equal Psec
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Transformers
Current
• The ideal transformer does not dissipate power.
• Power delivered from the source is passed on to the load
by the transformer.
The ideal
transformer turns
ratio equation for
current is
n
I pri
I sec
Notice that the primary
current is in the
numerator.
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Transformers
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Transformers
Non-ideal transformers
Operational losses occur due to:
Winding resistance (causing power to be dissipated in the
windings.)
Hysteresis loss (due to the continuous reversal of the magnetic
field.)
Core losses due to circulating current in the core (eddy currents).
Winding capacitance that has a bypassing effect for the windings.
Flux leakage where boundary flux from the primary that does not
link to the secondary
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Transformers
Power Ratings
• The power-handling capacity of a transformer is dependent
upon its ability to dissipate heat.
• If the heat can safely be removed, the power-handling
capacity of the transformer can be increased.
• This is sometimes accomplished by immersing the
transformer in oil, or by the use of cooling fins or both.
• The power-handling capacity of a transformer is measured
in either the volt-ampere unit or the watt unit.
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Transformers
Transformer efficiency
The efficiency of a transformer is the ratio of power
delivered to the load (Pout) to the power delivered to the
primary (Pin).
 Pout
 
 Pin

100%

  eta
What is the efficiency of the transformer?
20 mA
Vpri
120 Vrms
15 Vrms
RL
100 W
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Transformers
Transformer efficiency
 VL 2

 15 V 2

 Pout 


R
100 W 100%  94%
L
 

100%  
100%


 120 V  0.020 A  
 Pin 
 Vpri  I pri  




What is the efficiency of the transformer?
20 mA
Vpri
120 Vrms
15 Vrms
RL
100 W
94%
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Transformers
Example 2
•
Example 2: You have a transformer that’s primary power is 150W. If
10.5 W are dissipated in the winding resistances, what is the output
power to the load, neglecting any other losses?
•
What is the efficiency of the above transformer?
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Transformers
Tapped and multiple-winding transformers
• It is possible to use multiple taps (connection points)
on a transformer to achieve different voltage ratings.
• Can be either on the primary side or the secondary
side or both.
Secondary with
center-tap
Primary with multiplewindings
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Transformers
Tapped and multiple-winding transformers
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Transformers
Tapped and multiple-winding transformers
Different taps, on the primary side, determine the voltage
delivered to the customer.
The center-tapped
secondary allows
household wiring
to select either 120
V or 240 V.
Transformer
7200 V
120 V
CT Ne
utral
120 V
Service
entrance
Building
120 V
240 V
120 V
Distribution
or breaker box
Earth
ground
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Transformers
Tapped
Tappedand
andmultiple-winding
multiple-windingtransformers
transformers
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Transformers
Three-phase transformers
• Three-phase power is used for power transmission and
industrial applications.
• Voltages in a three-phase system can be transformed with
1. three identical single phase transformers or
2. one three-phase transformer.
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Transformers
Three-phase transformers
Three-phase transformers are wired in either a wye or a delta
configuration or a combination of both.
This transformer is a
wye-to-delta
configuration, which is
generally used in step
down cases.
Vpri
Three-phase
wye to delta
transformer
Vsec
The delta-wye (not
shown) is generally
used in step up cases.
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Transformers
Three-phase transformer combinations
Delta to Wye
Delta to Delta
Wye to Delta
Wye to Wye
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Transformers
Converting three-phase utility voltages to
single-phase residential voltages.
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Transformers
Selected Key Terms
Mutual The inductance between two separate coils, such
inductance as in a transformer.
Transformer An electrical device constructed of two or more
coils that are magnetically coupled to each
other so that there is mutual inductance from
one coil to the other.
Primary The input winding of a transformer; also
winding called primary.
Secondary The output winding of a transformer; also called
winding secondary.
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Transformers
Selected Key Terms
Magnetic The magnetic connection between two coils as
coupling a result of the changing magnetic flux lines of
one coil cutting through the second coil.
Turns ratio The ratio of the turns in the secondary
winding to the turns in the primary winding.
Reflected The resistance of the secondary circuit
resistance reflected into the primary circuit.
Impedance A technique used to match a load resistance to a
matching source resistance in order to achieve maximum
transfer of power.
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Transformers
Quiz
2. A step-up transformer refers to one in which
a. the voltage across the secondary is higher than
the primary.
b. the current in secondary is higher than the
primary.
c. the power to the load is higher than deleivered to
the primary.
d. all of the above.
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Transformers
Quiz
3. An isolation transformer
a. blocks both ac and dc.
b. blocks ac but not dc.
c. blocks dc but not ac.
d. passes both ac and dc.
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Transformers
Quiz
4. If the current in the secondary is higher than in the
primary, the transformer is a
a. a step-up transformer.
b. an isolation transformer.
c. a step-down transformer.
d. not enough information to tell.
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Transformers
Quiz
5. An ideal transformer has
a. no winding resistance.
b. no eddy current loss.
c. power out = power in.
d. all of the above.
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Transformers
Quiz
7. A transformer that can deliver more power to the load
than it receives from the source is a(n)
a. step-up type.
b. step-down type.
c. isolation type.
d. none of the above.
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Transformers
Quiz
10. A transformer that could be used for 110 V or 220 V
operation is a
a. multiple-winding type.
b. center-tapped type.
c. isolation type.
d. all of the above.
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