TOPIC 4 - Transformer

DET20033-ELECTRICAL CIRCUITS
TOPIC 4:

TRANSFORMER

Reference : CHAPTER 21

Electrical and Electronic Principles and Technology
Third edition

John Bird BSc(Hons), CEng, CSci, CMath, FIET, MIEE,
FIIE, FIMA, FCollT

COURSE LEARNING

OUTCOMES

• Understand mutual inductance [CLO1]
• Understand the construction and the

operation of a transformer [CLO1]

• Understand how transformer increases and

decreases voltage [CL01]

• Understand the effect of a resistive load

across the secondary winding [CLO1]

• Understand a non-ideal transformer [CLO1]
• Understand several types of transformers

[CLO1]

BASIC TRANSFORMER

A transformer is a device which uses Circuit diagram
the phenomenon of mutual induction
to change the values of alternating
voltages and currents.

Schematic Symbols

TYPES OF CORE

❑ The windings of a transformer are formed around the
core.

❑ The core provides both a physical structure for
placement of the windings and a magnetic path so
that the magnetic

❑ Flux is concentrated close to the coils.

Transformer type
symbols

Mutual Inductance

Self inductance L : When the e.m.f. is induced in the same
circuit as hat in which the current is changing
Mutual inductance,M : When the e.m.f. is induced in a circuit
by a change of flux due to current changing in an adjacent
circuit

Factor that affect MUTUAL INDUCTANCE

Magnetic coupling

❑ 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 windings.

❑ The tighter the coupling, the greater the induced voltage
in the secondary for a given Current in the primary.

ELECTRICAL ISOLATION

❑ When two coils are magnetically coupled, they provide
electrical isolation because there is no electrical
connection between them, only a magnetic link.

Coefficient of Coupling

❑ The coefficient of coupling, k, between two coils is the ratio of the
magnetic lines of force (flux) produced by coil I linking coil 2 to the total
flux produced by coil I

❑ The COEFFICIENT OF COUPLING of a transformer is dependent on
the portion of the total flux lines that cuts both primary and secondary

windings.

❑ Ideally, all the flux lines generated by the primary should cut the
secondary, and all the lines of the flux generated by the secondary
should cut the primary.

❑ The coefficient of coupling would then be one (unity), and maximum
energy would be transferred from the primary to the secondary.

❑ The coefficient of coupling, k, depends on the physical closeness of the
coils and the type of core material on which they are wound. Also, the
construction and shape of the cores are factors.

TURN RATIO

The ratio of the number of turns in the secondary winding
(N2) to the number of turns in the primary winding (N1)

The Step-Up Transformer

A transformer in which the secondary voltage is greater than
the primary voltage is called a step-up transformer. N1<N2

The Step-Down Transformer

A transformer in which the secondary voltage is less than
the primary voltage is called a step-down transformer.
N2<N1

The relationship between
primary and secondary

voltages

The ratio of secondary voltage (V2) to primary voltage (V1)
is equal to the ratio of the number of turns in the secondary
winding (N2) to the number of turns in the primary winding
(N1).

***Isolation transformer : N1=N2

EXERCISE

Problem 1.
The transformer in Figure 1 has a turns ratio of 3. What
is the voltage across the secondary winding? (360v)

EXERCISE

Problem 2.
The transformer in Figure 14-11 has a turns ratio of 0.2.
What is the secondary voltage? (24v)

EXERCISE

Problem 3.
A primary voltage of 120v is

reduced to 12v
ac. What is the turn ratio? (0.1)

EXERCISE

Problem 4.
A transformer has 500 primary turns and
3000 secondary turns. If the primary

voltage
Is 240V, determine the secondary

voltage,
Assuming an ideal transformer. (1440v)

EXERCISE

Problem 5.
An ideal transformer has a turns

ratio of 8:1
and the primary current is 3A when

it is
supplied at 240V. Calculate the

secondary
Voltage and current.(30V, 24A)

EXERCISE

Problem 6.
An ideal transformer, connected to a
240V mains, supplies a 12V, 150W lamp.
Calculate the transformer turns ratio and the
Current taken from the supply.(0.05, 0.625A)

EXERCISE

Problem 7.
A 12Ω resistor is connected across the
secondary winding of an ideal transformer
whose secondary voltage is 120V. Determine
The primary voltage if the supply current is
4A. (300v)

POWER IN TRANSFORMER

❑ For an ideal transformer, the power delivered to the
primary equals the power delivered by the secondary to

the load.
❑ When losses are considered, some of the power is

dissipated in the transformer rather than the load;
therefore, the load power is always less than the power
in the primary.
❑ Power is dependent on voltage and current, and there
can be no increase in power in a transformer.
❑ Therefore, if the voltage is stepped up, the current is
stepped down.

Transformer Losses And
Efficiency

• Two sources of losses in transformers
on load:

1. Copper losses
2. Iron losses

1. Copper losses

• are variable and result in a heating of the
conductors.

• If R1 and R2 are the primary and secondary
winding resistances then the total copper loss is
I12.R1 + I22.R2

1. Iron losses

• are constant for a given value of frequency and
flux density and are of two types - hysteresis loss
and eddy current loss.

• A 5 kVA single-phase transformer has a turns ratio of 10:1 and is fed from a
2.5 kV supply. Neglecting losses, determine

(a) the full-load secondary current,
(b) the minimum load resistance which can be connected across the

secondary winding to give full load kVA,
(c) the primary current at full load kVA.



Transformer Efficiency

• Transformer efficiency formula:

• It is not uncommon for power transformers
to have efficiencies of between 95% and
98%.

• Therefore :

1. Output Power = V2I2CosΦ2
2. Total losses = copper loss + iron losses
3. Input power = output power + losses

EXERCISE

Problem 1

• A 200 kVA rated transformer has
a full-load copper loss of 1.5kW
and an iron loss of 1kW.
Determine the transformer
efficiency at full load and 0.85
power factor.
Ans : (0.9855 or 98.55%)

EXERCISE

Problem 2
• A 400 kVA transformer has a primary winding

resistance of 0.5 and a secondary winding
resistance of 0.001. The iron loss is 2.5kW and
the primary and secondary voltages are 5 kV
and 320V respectively. If the power factor of the
load is 0.85, determine the efficiency of the
transformer:

(a) on full load.

(b) on half load.

Ans : (a) 97.91%, (b) 97.87%

TYPES OF
TRANSFORMER

❑ center-tapped transformer
❑ multiple-winding transformers
❑ autotransformers

Center Tapped Transformer

• A transformer with a “tap” in the center of the secondary winding.

• This “tap” or additional connection in the middle of the winding can
be used with, or instead of, other types of connections at the ends of
the windings. This scenario provides a variety of winding ratios.

• used as a ground, neutral, connection and provide an option to use
full voltage or half on the secondary side. Each side can provide half
of the output capacity of the secondary side that they split.

• Single phase center tap transformers are often utilized in residential
and commercial building electrical applications.

• Three phase center tap transformers are generally utilized for
smaller, auxiliary loads. Other applications where Center Tap
Transformers are commonly utilized include the following power
source applications:

Center Tapped Transformer
circuit diagram

Center Tapped Transformer Application

• Audio power amplifier – center tap transformers are
utilized to drive push-pull output stages. Small amounts
of direct current may pass through the winding and
these audio output transformers are specifically
designed to tolerate this occurrence.

• Rectifier – a full-wave rectifier is created with a center
tap transformer and two diodes. This configuration is
smoother than a half-wave rectifier because both half
cycles of the AC waveform contribute to the direct
current. This configuration is commonly found in vacuum
tube equipment and high current applications such as
large, auto, battery chargers.

• Phase splitter – with electric amplifiers, center trap
transformers allow the flexibility of coupling at different
stages.

Multiple Winding Transformer

• Three inductor coils share a common magnetic core,
magnetically “coupling” or “linking” them together.

• The relationship of winding turn ratios and voltage ratios seen
with a single pair of mutual inductors still holds true here for
multiple pairs of coils.

• Not only are voltages and currents of completely different
magnitudes possible with such a transformer, but all circuits
are electrically isolated from one another.

• The transformer is intended to provide both high and low
voltages necessary in an electronic system using vacuum
tubes.

• If electrical isolation between secondary circuits is not of great
importance, a similar effect can be obtained by “tapping” a
single secondary winding

Multiple Winding Transformer
circuit diagram

• It is a Auto Transformers

transformer which has part of its

winding common to the primary and

secondary circuits.

Fig. (a) : shows the circuit for a Fig. (b) : that for an auto transformer
doublewound transformer

Auto Transformers circuit
diagram

Advantages of Auto

Transformers

• The advantages of auto transformers

over doublewound transformers
include:
1. a saving in cost since less copper is

needed.

2. less volume, hence less weight.
3. a higher efficiency, resulting from lower

I2R losses.

4. a continuously variable output voltage is

achievable if a sliding contact is used a
smaller percentage voltage regulation.

Disadvantages of Auto
Transformers

• The primary and secondary windings are
not electrically separate, hence if an open-
circuit occurs in the secondary winding the
full primary voltage appears across the
secondary.

Uses of Auto Transformers

• Are used for :
1. Reducing the voltage when starting
induction motors.
2. For interconnecting systems that are
operating at approximately the same
voltage.

• Isolating Transformers

Transformers not only enable current or voltage

to be transformed to some different magnitude

but provide a means of isolating electrically one

part of a circuit from another when there is no

electrical connection between primary and

secondary windings.

• An isolating transformer is a 1:1 ratio
transformer with several important applications,
including bathroom shaver-sockets, portable
electric tools, model railways, and so on.

Non-ideal transformer
characteristics

✔ the transformer windings are resistance
less

✔ it has infinite permeability so it requires
zero mmf to produce flux

✔ the leakage flux is negligible
✔ the core loss is also negligible