1. Principles & Applications
Electricity
Principles & Applications
Sixth Edition
Richard J. Fowler
Chapter 12
Transformers
© Glencoe/McGraw-Hill

2. INTRODUCTION Transformer Fundamentals Transformer Efficiency
Loaded Transformers
Three-phase Transformers
Impedance Matching

3. Facts About Transformers
Transformers operate on mutual inductance.
A transformer has a primary winding and a secondary winding.
The coefficient of coupling is the portion of primary flux that links the secondary.
With 100% coupling, the turns-per-volt ratio is the same for all windings.
Transformers can have hysteresis, eddy current, and copper (I2R) losses.

4. More Facts About Transformers
Transformer losses can be reduced by using silicon steel cores, laminated cores, and small gage wires.
As the load on a transformer increases, angle theta decreases.
Three-phase transformers use a three-legged core.
Transformer windings can be connected in series or parallel.

5. Transformer Fundamentals
Primary
Secondary
Load
A transformer has a primary coil
and a secondary coil.
The primary is connected to a source.
The secondary is connected to a load.
During the first half-cycle,
the flux builds up and collapses.
This creates a half-cycle of induced voltage in the secondary.

6. Transformer Fundamentals
Primary
Secondary
Load
During the next half-cycle,
the flux again builds up and collapses.
This creates another half-cycle of induced voltage in the secondary.
Notice that the primary and secondary voltages are out-of-phase.

7. Primary-Secondary Terminology
Transformers are bidirectional devices.
120 V
Primary
Source
90 V
Secondary
Load
This transformer was designed to step 120 V down to 90 V.
120 V
Secondary
Load
Source
90 V
Primary
However, either winding can be used as the primary.

8. Turns-Per-Volt Ratio _ + 0.25 V + 1.0 V _ _ 0.75 V +
The 4-turn primary with a 1 volt source provides 4 turns-per-volt;
therefore, each turn has 0.25 V across it.
Each turn will produces a specific amount of flux in the core.
This same flux will, in turn, produce 0.25 V in each secondary turn.
Thus, a 1 turn secondary provides 0.25 V,
and a 3 turn secondary provides 0.75 V.

9. Eddy Current Illustration
If an eddy current is induced in the core, one will also be induced
in the aluminum disk placed on top of the core. The eddy current in
the aluminum disk will produce a magnetic field that opposes the
field that created the eddy current.
Eddy current
Aluminum disk
Coil connected to
a 60-Hz supply
The next slide shows the results of the eddy current in the aluminum.

10. Click on the image to run the display.
To rerun the display, click again on the image.

11. Transformer Losses
Copper (I2R) loss B H
Hysteresis loss (green area of the hysteresis loop)
Eddy current loss
(I2R in the core)
These losses are minimized by a narrow hystersis loop, thin laminations, and large diameter wire.

12. Transformer Efficiency
Source
provides
1640 W
Transformer
90 W loss
(heat loss)
Load
1550 W
consumed
The transformer core and copper losses cause the transformer to heat up as electric energy is converted to heat energy.
Efficiency = 1550 W / 1640 W =

13. Transformer-Action Quiz
The ____ coil of a transformer is
connected to the source.
primary
Flux builds and collapses in a core ____
time(s) each cycle.
two
A transformer provides ____ degrees of
phase shift between its two windings.
180
Any winding of a transformer can be used
as the ____ winding.
primary
(or secondary)
Core losses can be reduced by using ____
laminations.
thinner
Transformer inefficiency is caused by core
and ____ losses.
copper

14. Primary Current Load Iref Ipri With no load, Ipri is the
Vpri
Vpri
Ipri
Ien
Ipri
With no load, Ipri is the
energizing current (Ien).
With a load, Ipri
is composed of Ien
and Iref .
The transformer acts like an inductor.
Iref is the resistive load current reflected from the secondary to the primary.
Theta is large; power is low.

15. There is no phase-1 flux because phase-1 current is zero.
Flux in a Three-Phase Core
Core
Phase 3
Phase 1
Phase 2
Time 1
Phase 1
coil 2 3
At time 1,
flux created by phase 2
and phase 3
join together.
There is no phase-1 flux because phase-1 current is zero.

16. Flux in a Three-Phase Core
(Time 2)
Core
Phase 3
Phase 1
Phase 2
Time 2
Phase 1
coil 2 3
At time 2,
flux created by phase 2 and phase 3 still join together.
Also, flux created by phase 1
and phase 2
join together.

17. Flux in a Three-Phase Core
(Time 3)
Core
Phase 3
Phase 1
Phase 2
Phase 1
coil 2 3
Time 3
At time 3,
flux created by phase 1 and phase 2 still join together.
Also, flux created by phase 1
and phase 3
join together.

18. Flux in a Three-Phase Core
(Time 4)
Core
Phase 3
Phase 1
Phase 2
Phase 1
coil 2 3
Time 4
At time 4,
flux created by phase 1 and phase 3 still join together.
Also, flux created by phase 2
and phase 3
join together.

19. Primary-Current Quiz The no-load primary current is called
the ____ current.
energizing
The additional primary current caused by loading
the transformer is called the ____ current.
reflected
(or resistive)
Angle theta ____ when a load is
connected to a transformer.
decreases
A transformer with no load acts like a(n) ____.
inductor
In a three-phase transformer, at least ____
primary coils are creating flux at any instant.
two

20. Series-Opposing Windings
120 V + _
8 V
2 A
6 V
3 A
2 V _ +
2 A
Connect two terminals with the same instantaneous polarities.
Take the output from the other two terminals.
The output voltage equals the difference between the two voltages.
The current is limited to the lesser of the two winding currents.

21. Series-Aiding Windings
120 V + _
8 V
2 A
6 V
3 A
14 V _ +
2 A
Connect two terminals that have opposite instantaneous polarities.
Take the output from the other two terminals.
The output voltage equals the sum of the two winding voltages.
The current is limited to the lesser of the two winding currents.

22. Parallel Secondary Windings
120 V + _
9 V
4 A
9 V _ +
8 A
The two windings must have equal voltage ratings.
The two windings should have equal current ratings.
Connect the negative terminals
and the positive terminals.
Take the output from the negative and positive terminals.
Voutput = Vwinding and
Ioutput = 2 x Iwinding

23. Impedance Matching 10:1 ratio 100 W 1 W 0.1 A 1 A 10 V 1 V 20 V 100 W
Notice the source in both circuits
provides 0.1 A at 10 V. Thus, the
transformer makes the 1-W resistor
act like a 100-W resistor in terms
of the load on the source.

24. Series and Parallel-Windings Quiz
Series-opposing windings produce a voltage equal
to the ____ of the voltages of the two windings.
difference
series-
The current rating of ____ connected windings is
that of the winding with the smallest current rating.
A 12-V, 2-A secondary series aiding a 6-V, 3-A
secondary will provide ____ V and ____ A.
18, 2
For parallel windings, ____ instantaneous polarities
should be connected together.
like
Parallel windings must have equal ____ ratings.
voltage
A transformer used to make a load appear to be other
than its true value is called a(n) ____ ____ transformer.
impedance-
matching

25. REVIEW Transformer Fundamentals Transformer Efficiency
Loaded Transformers
Three-phase Transformers
Impedance Matching