1 Introduction to Transformers
Transformer design and test are sometimes viewed as an art rather than a
science.
Transformers are imperfect devices, and there will be differences between
a transformer's design values, its test measurements, and its performance
in circuit.
By going back to basics, this tech note will help design and test
engineers understand how a transformer's electrical characteristics are
the result of physical properties of the core and windings.
A partner tech note, "Transformer Testing Basics", describes how these
characteristics are measured in order to confirm that a transformer has
been correctly manufactured and how to avoid some of the common pitfalls
in making those measurements.
2 Basic Transformer Theory

The above figure represents the essential elements for a transformer: a
magnetic core with a primary and secondary coil wound on the limbs of the
magnetic core.
An alternating voltage (Vp) applied to the PRIMARY creates an
alternating current (Ip) through the primary.
This current produces an alternating magnetic flux in the magnetic core.
This alternating magnetic flux induces a voltage in each turn of the
primary and in each turn of the secondary.
As the flux is a constant, i.e. the same in both primary and secondary:
This equation shows that a transformer can be used to step up or step
down an ac voltage by controlling the ratio of primary to secondary turns.
(Voltage transformer action).
It can also be shown that:
Primary Volt Amperes = Secondary Volt Amperes
This equation shows that a transformer can be used to step up or step
down an ac current by controlling the ratio of primary to secondary turns.
(Current transformer action)
It will be noted that there is no electrical connection between the
primary and secondary windings. A transformer, therefore, provides a means
of isolating one electrical circuit from another.
These features - voltage/current transformation and isolation - cannot be
obtained efficiently by any other means, with the result that transformers
are used in almost every piece of electrical and electronic equipment in
the world.
3 B-H curves
When the primary of a transformer is energized with the secondary
unloaded, a small current flows in the primary. This current creates a
'magnetizing force' that produces the magnetic flux in the transformer
core.
The magnetizing force (H) is equal to the product of magnetizing current
and the number of turns, and is expressed as Ampere - Turns.
For any given magnetic material, the relationship between magnetizing
force and the magnetic flux produced can be plotted. This is known as the
B-H curve of the material.
From the B-H curve it can be seen that, as the magnetizing force is
increased from zero, the flux increases up to a certain maximum value of
flux.
Above this level, further increases in magnetizing force result in no
significant increase in flux. The magnetic material is said to be
'saturated'.
A transformer is normally designed to ensure that the magnetic flux
density is below the level that would cause saturation. The flux density
can be determined using the following equation:
Where:
E represents the rms value of the applied voltage.
N represents the number of turns of the winding.
B represents the maximum value of the magnetic flux density in the core
(Tesla).
A represents the cross-sectional area of the magnetic material in the core
(sq. meters).
f represents the frequency of the applied volts.
Note
1 Tesla = 1 Weber/meter²
1 Weber/m² = 10,000 Gauss
1 Ampere-turn per meter = 4p x 10-3 Oersteds
In practice, all magnetic materials, once magnetized, retain some of
their magnetization even when the magnetizing force is reduced to zero.
This effect is known as 'Remanence' and results in the B-H curve for the
material exhibiting a response to a decreasing magnetizing force that is
different to the response to an increasing magnetizing force.
In practice, then, real magnetic materials have a B-H curve as follows:
The curve shown above is termed the 'hysteresis' loop of the material,
and it represents the true B-H response of the material. (The B-H curve
shown in figure 2 represented the average or mean of the true B-H loop
response).
The slope of the B-H curve, the saturation level, and the size of the
hysteresis loop are dependent on the type of material used, and on other
factors. This is illustrated using the following examples:
 |
Low-grade iron core
High-saturation flux density
Large loop = large hysteresis loss
Suitable for 50/60Hz |
 |
High-grade iron core
High-saturation flux density
Medium loop = medium hysteresis loss
Suitable for 400Hz transformers |
 |
Ferrite core - no air gap
Medium-saturation flux density
Small loop = small hysteresis loss
Suitable for-high frequency transformers |
 |
Ferrite core - large air gap
Small loop = small hysteresis loss
Suitable for high-frequency Inductors with large DC current |
4 Hysteresis Loss
Hysteresis loss is the result of cycling the magnetic material along its
B-H curve.
It represents the energy taken as the applied voltage, aligns magnetic
dipoles first in one direction, and then in the other.
The loss increases with the area of the B-H curve enclosed. As the
material is driven closer to saturation, both the area within the curve,
and the corresponding energy loss each cycle, increase substantially.
5 Eddy Current Loss
Eddy current loss is caused by small currents circulating within the core
material, stimulated by the alternating flux in the core.
The I2R power loss associated with these currents produces
heating of the core known as eddy current loss.
In iron-cored transformers, insulated iron sheets known as laminations
are used to minimize this effect by restricting the path for circulating
currents.
Ferrite cores restrict these paths even further.

6 Transformer Equivalent Circuit
An ideal transformer with one primary winding and two secondary windings
can be represented as shown below
Such a transformer has the following characteristics:
• No losses
• Perfect coupling between all windings
• Infinite open circuit impedance (i.e., no input current when secondaries
are open-circuited).
• Infinite insulation between windings
In reality, practical transformers show characteristics that differ from
those of an ideal transformer. Many of these characteristics can be
represented by a transformer equivalent circuit:
Where:
• R1, R2, R3 represent the resistance of the winding wire.
• C1, C2, C3 represent the capacitance between the windings.
• Rp represents the losses which are due to the eddy current and
hysteresis losses. These are the real power losses, sometimes called the
core loss, that may be measured by performing an open-circuit power
measurement. Because there is no load current, there is very little I2R
copper loss in the energized winding, and the watts measured at no load
are nearly all due to the core.
• Lp represents the impedance due to the magnetizing current. This is
the current that generates the magnetizing force, H, used in the B-H loop
diagrams. Note that this current may not be a simple sine wave, but can
have a distorted, peaked shape, if the transformer is operated in the
non-linear region of the B-H curve. This is usually the case for
line-frequency, laminate type transformers.
• L1 L2 L3 represents the leakage inductance of all the windings. (This
is discussed in detail in Voltech Note 104-105, "Leakage Inductance".)
7 Conclusions
The equivalent circuit of a transformer reflects the real properties of
the magnetic circuit comprising the core and windings.
The equivalent circuit can therefore be used with confidence to
understand and predict the transformer's electrical performance in a
variety of situations.
8 Further Reading
The equivalent circuit can also be used to help understand and optimize
the tests and test conditions that can be used to check that a transformer
has been constructed correctly.
Further technical notes in this series discuss how the equivalent circuit
parameters are used to derive practical tests for transformers to
guarantee their quality in a manufacturing environment.
See also:
Leakage Inductance Tech Note (VPN 104-105)
Turns Ratio Tech Note (VPN 104-113 )
Ferrite Transformer Testing Tech Note (VPN 104-128)
Laminate Transformer Testing Tech Note (VPN 104-127)
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