An Introduction to Tranformers:
Definition, Calculations, and Applications
Adam Rusenko
Introduction
From turning on a light switch to charging your phone, you use electricity each and every day.
Most people utilize this resource without ever thinking of how the power gets to the outlet. Is it
as simple as a few power lines? In fact, the process of providing electricity at an affordable rate
is a detailed process. A vital component of this process is the electrical transformer.
Transformers are one aspect to making electrical energy transmission an efficient and affordable
solution to power. In this section, we will discuss the transformer, including its purposes and
applications.
What is a Transformer?
Contrary to popular belief, a transformer is not a robot in disguise. An electrical transformer is
an electrical device used to manipulate the voltage and current of a signal in a transmission line.
The transformer fundamentally involves many coils wrapped around an iron core. These devices
are most commonly used in electric power distribution, and can be found in a variety of sizes and
parameters. The main purpose of a transformer is
to control the power flow within the line in order
to assure efficient transportation with minimal
losses.
How does it Work?
As mentioned above, a transformer is mainly
comprised of an iron core, and coil windings on
either side. This configuration takes advantage of
the changing magnetic flux in the transformer
core to adjust the voltage of a signal. Figure 1 is a
Figure 1
useful representation of the inside of a
transformer. An electric signal would enter the
transformer at the wire labeled ‘primary current’. The current that travels through the primary
coils induces a magnetic field in the transformer core. As you may recall from physics courses,
voltage is created by a varying magnetic field. This voltage will correspond to the secondary
voltage, and in turn, an induced current (Is) will arise in the secondary winding. By controlling
the number of primary and secondary coil windings, we can manipulate the secondary voltage
and current of the electrical signal.
The relationship between primary and secondary voltages and currents in an ideal transformer is
defined by the ratio of secondary windings to primary windings. These equations are shown
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below, where N1 is the number of primary windings, and N2 is the number of secondary
windings.
𝑵𝒑
𝑵𝒔
𝑽𝒐𝒍𝒕𝒂𝒈𝒆 ∶ 𝑽𝒔 =
𝑽𝒑
𝑪𝒖𝒓𝒓𝒆𝒏𝒕: 𝑰𝒔 =
𝑰
𝑵𝒑
𝑵𝒔 𝒑
A transformer is considered a step- down transformer if the secondary voltage is less than the
primary voltage, or N2/N1 is less than one. Congruently, in a step-up transformer, the
secondary voltage will be larger than the primary voltage, or N 2/N1 is greater than one. For our
considerations in this section, we will not worry about the non-ideal characteristics of a
transformer.
Transformer Calculation Example
The circuit in Figure 2 demonstrates an 8 Ω load
with line losses shown as a 2 Ω resistor. Notice that
this circuit does not include a transformer. Using
Ohm’s Law to solve for the current, we can find
the power dissipated in the load resistor using P = i 2R.
As shown in the figure, 8 Watts are dissipated across
the load.
Figure 2
Now we will add an ideal transformer to the same
circuit. The numbers below the transformer are the
windings. In this case, the primary winding N1=.5
and the secondary winding N2= 1, making the ratio
N2/N1 = 1/.5 = 2. Next, we draw the equivalent circuit
by adjusting the load resistance with the turns ratio.
From the ideal transformer equations we know that:
𝑵𝒑
𝑵𝒔
𝑽𝒐𝒍𝒕𝒂𝒈𝒆 ∶ 𝑽𝒔 =
𝑽𝒑
𝑪𝒖𝒓𝒓𝒆𝒏𝒕: 𝑰𝒔 =
𝑰
Figure 3
𝑵𝒔
𝑵𝒑 𝒑
Similarly, we can apply Ohm’s Law to find a relationship for the load resistor. We can find
the equivalent resistance:
𝑵𝒑
𝑵𝒑
𝑽𝒔 𝑵 𝒔 𝑽𝒑
𝑹𝒔 = 𝟖Ω =
=
= ( )𝟐 𝑹𝒑 = (𝟐)𝟐 𝑹𝒑 = 𝟒𝑹𝒑 = 𝟖Ω
𝑵𝒔
𝑰𝒔
𝑵𝒔
𝑵𝒑 𝑰𝒑
From the equation above, we see that if we move the 8 Ω resistor to the primary side of the
transistor, it will act as a 2 Ω resistor. Now we can solve for the power across the load just
like the previous example. From Figure 3, we find the power across the load resistor
becomes 12.5 Watts compared to the 8 Watts in the first example.
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Transformer Applications
Transformers have a wide variety of applications, but
are mainly used in power transmission and
distribution. As you may know from other classes,
power losses in a transmission line are directly
related to the square of the current multiplied by the
resistance (i2R). In order to minimize the losses in
power lines, transformers are used to reduce the
current in the line. A step-up transformer is used
initially when an electrical signal is generated so that
the current in the line will be low. However, this
Figure 4
means the signal will travel with an extremely high
voltage, which can be dangerous and lethal. Figure 4 shows an example of such a transformer,
which would be used for long-distance transmission. These transformers will increase the
voltage of a signal to around 230 kV. Once the signal approaches
its destination, a neighborhood for example, a step down
transformer is used to change the signal back to a higher current
and lower voltage around 7200 V. However, another step-down
transformer is needed to decrease the signal to a value we can
from our homes. Figure 5 shows the step down transformer that
will be used to decrease the voltage from 7200 V to the 240 V we
need for household appliances.
Figure 5
Conclusion
Transformers are a vitally important component in electrical power transmission because they
help to control power flow by adjusting voltages and currents. While this section provided a very
basic understanding of transformers, many comprehensive resources exist. Any electrical
engineers with an interest in power systems or energy will certainly study further topics with
transformers such as the non-ideal characteristics and implementation in multi-phase systems.
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Audience & Scope:
My target audience for this description will be inexperienced electrical engineering students that
are being introduced to transformers. I will assume that they have acquired some basic
knowledge in electrical engineering, such as voltage and current, but are unfamiliar with
transformers and their applications. This document would likely be published in a textbook used
in a college level course. It will provide an introduction to transformers including how they
function, and how they are applied in real life. I will also include some simple transformer
calculations that are not comprehensive, but will be sufficient for a simple understanding.
Sources:
http://energyquest.ca.gov/how_it_works/transformer.html
Figure 1: http://en.wikipedia.org/wiki/Transformer
Figure 2,3: ©Jeffrey Mayer 2005-2015
Figure 4: http://www.mgmelectricalsurplus.com/Details/Transformers/Substation/265.php
Figure 5: http://science.howstuffworks.com/environmental/energy/power9.htm
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