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Transformer Basics
The Transformers
• Transformers are electrical devices consisting
of two or more coils of wire used to transfer
electrical energy by means of a changing
magnetic field.
• One of the main reasons that we use
alternating AC voltages and currents in our
homes and workplace’s is that AC supplies can
be easily generated at a convenient voltage,
transformed (hence the name transformer) into
much higher voltages and then distributed
around the country using a national grid of
pylons and cables over very long distances.
The Transformers
• The reason for transforming the voltage to a
much higher level is that higher distribution
voltages implies lower currents for the same
power and therefore lower 𝐼2
× 𝑅 losses along
the networked grid of cables.
The Transformers
• These higher AC transmission voltages and
currents can then be reduced to a much lower,
safer and usable voltage level where it can be
used to supply electrical equipment in our
homes and workplaces, and all this is possible
thanks to the basic Voltage Transformer.
The Transformers
• The Voltage Transformer can be thought of
as an electrical component rather. A
transformer basically is very simple static (or
stationary) electro-magnetic passive electrical
device that works on the principle of Faraday’s
law of induction by converting electrical
energy from one value to another.
The Transformers
• The transformer does this by linking together
two or more electrical circuits using a common
oscillating magnetic circuit which is produced
by the transformer itself. A transformer operates
on the principals of “electromagnetic
induction”, in the form of Mutual Induction.
The Transformers
• Mutual induction is the process by which a coil
of wire magnetically induces a voltage into
another coil located in close proximity to it.
• Then we can say that transformers work in the
“magnetic domain”, and transformers get their
name from the fact that they “transform” one
voltage or current level into another.
The Transformers
• Transformers are capable of either increasing
or decreasing the voltage and current levels of
their supply, without modifying its frequency,
or the amount of electrical power being
transferred from one winding to another via
the magnetic circuit.
The Transformers
• A single phase voltage transformer basically
consists of two electrical coils of wire, one called
the “Primary Winding” and another called the
“Secondary Winding”.
• We will define the “primary” side of the
transformer as the side that usually takes power,
and the “secondary” as the side that usually
delivers power.
• In a single-phase voltage transformer the primary
is usually the side with the higher voltage.
The Transformers
• These two coils are not in electrical contact
with each other but are instead wrapped
together around a common closed magnetic
iron circuit called the “core”.
• This soft iron core is not solid but made up of
individual laminations connected together to
help reduce the core’s losses.
The Transformers
• The two coil windings are electrically isolated
from each other but are magnetically linked
through the common core allowing electrical
power to be transferred from one coil to the
other.
• When an electric current passed through the
primary winding, a magnetic field is developed
which induces a voltage into the secondary
winding as shown:
The Transformers
Single Phase Voltage Transformer
• In a transformer there is no direct electrical
connection between the two coil windings,
thereby giving it the name also of an Isolation
Transformer.
Single Phase Voltage Transformer
• Generally, the primary winding of a
transformer is connected to the input voltage
supply and converts or transforms the
electrical power into a magnetic field.
• The job of the secondary winding is to convert
this alternating magnetic field into electrical
power producing the required output voltage as
shown:
Single Phase Voltage Transformer
Transformer Construction
(single-phase)
Where:
VP - is the Primary Voltage
VS - is the Secondary Voltage
NP - is the Number of Primary Windings
NS - is the Number of Secondary Windings
Φ (phi) - is the Flux Linkage
• A single-phase transformer can operate to either
increase or decrease the voltage applied to the
primary winding.
• When a transformer is used to “increase” the
voltage on its secondary winding with respect to
the primary, it is called a Step-up transformer.
• When it is used to “decrease” the voltage on the
secondary winding with respect to the primary it
is called a Step-down transformer.
Transformer Construction
(single-phase)
• A third condition exists in which a transformer
produces the same voltage on its secondary as
is applied to its primary winding, its output is
identical with respect to voltage, current and
power transferred.
• This type of transformer is called an
“Impedance Transformer” and is mainly used
for impedance matching or the isolation of
adjoining electrical circuits.
Transformer Construction
(single-phase)
• The difference in voltage between the primary
and the secondary windings is achieved by
changing the number of coil turns in the
primary winding ( NP ) compared to the
number of coil turns on the secondary winding
( NS ).
Transformer Construction
(single-phase)
• The transformer is basically a linear device, a
ratio now exists between the number of turns of
the primary coil divided by the number of turns of
the secondary coil.
• This ratio, called the ratio of transformation, more
commonly known as a transformers “turns ratio”,
( TR ).
• This value dictates the operation of the
transformer and the corresponding voltage
available on the secondary winding.
Transformer Construction
(single-phase)
• It is necessary to know the ratio of the number
of turns of wire on the primary winding
compared to the secondary winding. The turns
ratio, which has no units, compares the two
windings in order and is written with a colon,
such as 3:1 (3-to-1).
Transformer Construction
(single-phase)
• This means in this example, that if there are 3
volts on the primary winding there will be 1
volt on the secondary winding, 3 volts-to-1
volt.
• If the ratio between the number of turns
changes the resulting voltages must also
change by the same ratio, and this is true.
Transformer Construction
(single-phase)
• Transformers are all about “ratios”. The ratio of
the primary to the secondary, the ratio of the input
to the output, and the turns ratio of any given
transformer will be the same as its voltage ratio.
• In other words for a transformer: “turns ratio =
voltage ratio”. The actual number of turns of wire
on any winding is generally not important, just the
turns ratio and this relationship is given as:
Transformer Construction
(single-phase)
The Transformers Turns Ratio
•
𝑁𝑃
𝑁𝑆
=
𝑉𝑃
𝑉𝑆
= n Turns Ratio
• Assuming an ideal transformer and the phase
angles: ΦP ≡ ΦS
• Note that the order of the numbers when
expressing a transformers turns ratio value is
very important as the turns ratio 3:1 expresses
a very different transformer relationship and
output voltage than one in which the turns ratio
is given as: 1: 3
Transformer Basics Example
• A voltage transformer has 1500 turns of wire
on its primary coil and 500 turns of wire for its
secondary coil. What will be the turns ratio
(TR) of the transformer? .
• T.R. =
𝑁𝑃
𝑁𝑆
=
# 𝑃𝑟𝑖.𝐶𝑜𝑖𝑙𝑠
#𝑆𝑒𝑐.𝐶𝑜𝑖𝑙
=
1500
500
3
1
= 3 : 1
• This ratio of 3:1 (3-to-1) simply means that
there are three primary windings for every one
secondary winding.
• As the ratio moves from a larger number on
the left to a smaller number on the right, the
primary voltage is therefore stepped down in
value as shown:
Transformer Basics Example
Transformer Basics Example
• If 240 volts is applied to the primary winding
of the same transformer above, what will be
the resulting secondary no load voltage.
• T.R. = 3:1 or
3
1
=
𝑉𝑃
𝑉𝑆
=
# 𝑃𝑟𝑖.𝑉𝑜𝑙𝑡𝑠
#𝑆𝑒𝑐.𝑉𝑜𝑙𝑡𝑠
=
240
𝑉𝑆
• So Sec. Volts, 𝑉𝑆 =
𝑉𝑃
3
=
240
3
= 80 Volts
• Again confirming that the transformer is a
“step-down” transformer as the primary
voltage is 240 volts and the corresponding
secondary voltage is lower at 80 volts.
• Then the main purpose of a transformer is to
transform voltages at preset ratios and we can
see that the primary winding has a set amount
or number of windings (coils of wire) on it to
suit the input voltage.
Transformer Basics Example
• If the secondary output voltage is to be the
same value as the input voltage on the primary
winding, then the same number of coil turns
must be wound onto the secondary core as
there are on the primary core giving an even
turns ratio of 1:1 (1-to-1). In other words, one
coil turn on the secondary to one coil turn on
the primary.
Transformer Basics Example
• If the output secondary voltage is to be greater
or higher than the input voltage, (step-up
transformer) then there must be more turns on
the secondary giving a turns ratio of 1:N,
where N represents the turns ratio number.
• If it is required that the secondary voltage is to
be lower or less than the primary, (step-down
transformer) then the number of secondary
windings must be less giving a turns ratio of
N:1.
Transformer Basics Example

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Application of Residue Theorem to evaluate real integrations.pptx
 

LEC2 j.pdf

  • 2. The Transformers • Transformers are electrical devices consisting of two or more coils of wire used to transfer electrical energy by means of a changing magnetic field.
  • 3. • One of the main reasons that we use alternating AC voltages and currents in our homes and workplace’s is that AC supplies can be easily generated at a convenient voltage, transformed (hence the name transformer) into much higher voltages and then distributed around the country using a national grid of pylons and cables over very long distances. The Transformers
  • 4. • The reason for transforming the voltage to a much higher level is that higher distribution voltages implies lower currents for the same power and therefore lower 𝐼2 × 𝑅 losses along the networked grid of cables. The Transformers
  • 5. • These higher AC transmission voltages and currents can then be reduced to a much lower, safer and usable voltage level where it can be used to supply electrical equipment in our homes and workplaces, and all this is possible thanks to the basic Voltage Transformer. The Transformers
  • 6. • The Voltage Transformer can be thought of as an electrical component rather. A transformer basically is very simple static (or stationary) electro-magnetic passive electrical device that works on the principle of Faraday’s law of induction by converting electrical energy from one value to another. The Transformers
  • 7. • The transformer does this by linking together two or more electrical circuits using a common oscillating magnetic circuit which is produced by the transformer itself. A transformer operates on the principals of “electromagnetic induction”, in the form of Mutual Induction. The Transformers
  • 8. • Mutual induction is the process by which a coil of wire magnetically induces a voltage into another coil located in close proximity to it. • Then we can say that transformers work in the “magnetic domain”, and transformers get their name from the fact that they “transform” one voltage or current level into another. The Transformers
  • 9. • Transformers are capable of either increasing or decreasing the voltage and current levels of their supply, without modifying its frequency, or the amount of electrical power being transferred from one winding to another via the magnetic circuit. The Transformers
  • 10. • A single phase voltage transformer basically consists of two electrical coils of wire, one called the “Primary Winding” and another called the “Secondary Winding”. • We will define the “primary” side of the transformer as the side that usually takes power, and the “secondary” as the side that usually delivers power. • In a single-phase voltage transformer the primary is usually the side with the higher voltage. The Transformers
  • 11. • These two coils are not in electrical contact with each other but are instead wrapped together around a common closed magnetic iron circuit called the “core”. • This soft iron core is not solid but made up of individual laminations connected together to help reduce the core’s losses. The Transformers
  • 12. • The two coil windings are electrically isolated from each other but are magnetically linked through the common core allowing electrical power to be transferred from one coil to the other. • When an electric current passed through the primary winding, a magnetic field is developed which induces a voltage into the secondary winding as shown: The Transformers
  • 13. Single Phase Voltage Transformer
  • 14. • In a transformer there is no direct electrical connection between the two coil windings, thereby giving it the name also of an Isolation Transformer. Single Phase Voltage Transformer
  • 15. • Generally, the primary winding of a transformer is connected to the input voltage supply and converts or transforms the electrical power into a magnetic field. • The job of the secondary winding is to convert this alternating magnetic field into electrical power producing the required output voltage as shown: Single Phase Voltage Transformer
  • 16. Transformer Construction (single-phase) Where: VP - is the Primary Voltage VS - is the Secondary Voltage NP - is the Number of Primary Windings NS - is the Number of Secondary Windings Φ (phi) - is the Flux Linkage
  • 17. • A single-phase transformer can operate to either increase or decrease the voltage applied to the primary winding. • When a transformer is used to “increase” the voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. • When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer. Transformer Construction (single-phase)
  • 18. • A third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding, its output is identical with respect to voltage, current and power transferred. • This type of transformer is called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits. Transformer Construction (single-phase)
  • 19. • The difference in voltage between the primary and the secondary windings is achieved by changing the number of coil turns in the primary winding ( NP ) compared to the number of coil turns on the secondary winding ( NS ). Transformer Construction (single-phase)
  • 20. • The transformer is basically a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. • This ratio, called the ratio of transformation, more commonly known as a transformers “turns ratio”, ( TR ). • This value dictates the operation of the transformer and the corresponding voltage available on the secondary winding. Transformer Construction (single-phase)
  • 21. • It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). Transformer Construction (single-phase)
  • 22. • This means in this example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3 volts-to-1 volt. • If the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true. Transformer Construction (single-phase)
  • 23. • Transformers are all about “ratios”. The ratio of the primary to the secondary, the ratio of the input to the output, and the turns ratio of any given transformer will be the same as its voltage ratio. • In other words for a transformer: “turns ratio = voltage ratio”. The actual number of turns of wire on any winding is generally not important, just the turns ratio and this relationship is given as: Transformer Construction (single-phase)
  • 24. The Transformers Turns Ratio • 𝑁𝑃 𝑁𝑆 = 𝑉𝑃 𝑉𝑆 = n Turns Ratio • Assuming an ideal transformer and the phase angles: ΦP ≡ ΦS • Note that the order of the numbers when expressing a transformers turns ratio value is very important as the turns ratio 3:1 expresses a very different transformer relationship and output voltage than one in which the turns ratio is given as: 1: 3
  • 25. Transformer Basics Example • A voltage transformer has 1500 turns of wire on its primary coil and 500 turns of wire for its secondary coil. What will be the turns ratio (TR) of the transformer? . • T.R. = 𝑁𝑃 𝑁𝑆 = # 𝑃𝑟𝑖.𝐶𝑜𝑖𝑙𝑠 #𝑆𝑒𝑐.𝐶𝑜𝑖𝑙 = 1500 500 3 1 = 3 : 1
  • 26. • This ratio of 3:1 (3-to-1) simply means that there are three primary windings for every one secondary winding. • As the ratio moves from a larger number on the left to a smaller number on the right, the primary voltage is therefore stepped down in value as shown: Transformer Basics Example
  • 27. Transformer Basics Example • If 240 volts is applied to the primary winding of the same transformer above, what will be the resulting secondary no load voltage. • T.R. = 3:1 or 3 1 = 𝑉𝑃 𝑉𝑆 = # 𝑃𝑟𝑖.𝑉𝑜𝑙𝑡𝑠 #𝑆𝑒𝑐.𝑉𝑜𝑙𝑡𝑠 = 240 𝑉𝑆 • So Sec. Volts, 𝑉𝑆 = 𝑉𝑃 3 = 240 3 = 80 Volts
  • 28. • Again confirming that the transformer is a “step-down” transformer as the primary voltage is 240 volts and the corresponding secondary voltage is lower at 80 volts. • Then the main purpose of a transformer is to transform voltages at preset ratios and we can see that the primary winding has a set amount or number of windings (coils of wire) on it to suit the input voltage. Transformer Basics Example
  • 29. • If the secondary output voltage is to be the same value as the input voltage on the primary winding, then the same number of coil turns must be wound onto the secondary core as there are on the primary core giving an even turns ratio of 1:1 (1-to-1). In other words, one coil turn on the secondary to one coil turn on the primary. Transformer Basics Example
  • 30. • If the output secondary voltage is to be greater or higher than the input voltage, (step-up transformer) then there must be more turns on the secondary giving a turns ratio of 1:N, where N represents the turns ratio number. • If it is required that the secondary voltage is to be lower or less than the primary, (step-down transformer) then the number of secondary windings must be less giving a turns ratio of N:1. Transformer Basics Example