Introduction to Transformer
Transformer are crucial elements in both electrical and electronic systems, providing necessary electrical isolation and performing the essential function of altering voltages and currents. Although their design process is sometimes seen as an “art,” their construction and operation are grounded in fundamental physics principles.
A transformer is a device that transfers electrical energy from one alternating-current circuit to one or more other circuits, either increasing (stepping up) or decreasing (stepping down) the voltage. They are used for a variety of purposes, such as reducing the voltage of conventional power circuits to operate low-voltage devices like doorbells and toy electric trains, or increasing the voltage from electric generators to allow long-distance transmission of electric power.
Transformers modify voltage through electromagnetic induction. This occurs as magnetic flux lines build up and collapse with changes in the current passing through the primary coil, inducing current in another coil known as the secondary. The secondary voltage is determined by multiplying the primary voltage by the ratio of turns in the secondary coil to those in the primary coil, known as the turns ratio.
Air-core transformers are designed for transferring radio-frequency currents, which are used in radio transmissions; they consist of two or more coils wound around a solid insulating material or an insulating coil form. Iron-core transformers serve similar functions within the audio-frequency range. Impedance-matching transformers are utilized to align the impedance of a source with its load for optimal energy transfer. Isolation transformers are typically used for safety purposes to separate equipment from power sources.
Basic Transformer Theory
Transformers provide electrical isolation between circuits, which is vital for safety and functionality across various applications. A transformers comprises a magnetic core with primary and secondary coils wound around it. When an alternating voltage is applied to the primary coil, it generates an alternating current that corresponds to alternating magnetic flux within the core. This flux induces a voltage in both the secondary and primary coils, demonstrating Faraday’s Law of Induction.
The diagram above illustrates a transformer’s essential components: a magnetic core with primary and secondary coils wound on its limbs. An alternating voltage (Vp) applied to the primary creates an alternating current (Ip), producing alternating magnetic flux within the magnetic core. This flux induces voltage in each turn of both primary and secondary coils.
Since the flux remains constant across both primary and secondary:
This equation shows that by controlling the ratio of the number of primary turns to the number of secondary turns, the AC voltage can be increased or decreased (voltage conversion effect). It can also be demonstrated that: Primary Volt Amperes = Secondary Volt Amperes.
It can be seen from this that by adjusting the primary-secondary turns ratio, the AC current can also be increased or decreased (current conversion effect).It’s important to note there is no direct electrical connection between primary and secondary windings.
Transformers, therefore, provide a means of isolating one circuit from another. These functions (voltage/current transformation and isolation) cannot be effectively achieved by other means, so they are found in nearly every piece of electrical and electronic equipment in the world.
B-H Curves
The magnetic properties of core materials significantly influence transformers performance. When a transformer’s primary coil is energized, magnetizing current creates a magnetizing force (H), which generates magnetic flux (B) in the core. This relationship between B and H is depicted by the material’s B-H curve.The magnetizing force (H) equals the product of magnetizing current and turns number, expressed as Ampere-Turns. B-H curves illustrate how flux density changes as a function of magnetizing force; as H increases, B rises until saturation occurs in the core material. At saturation, further increases in H do not significantly increase B, making it crucial to design transformers to operate below saturation for efficiency.
From the B-H curve, it’s evident that as magnetizing force increases from zero, flux increases up to a maximum value. Beyond this level, further increases in magnetizing force do not significantly enhance flux; this state is termed ‘saturation.’ Transformers are typically designed to ensure magnetic flux density remains below saturation levels.
The flux density can be calculated using:
Where:
- EE represents RMS value of applied voltage.
- NN denotes winding turns.
- BB signifies maximum magnetic flux density (Tesla).
- AA indicates cross-sectional area of core material (sq. meters).
- ff stands for frequency of applied volts.
Note:
1 Tesla = 1 Weber/m²
1 Weber/m² = 10,000 Gauss
1 Ampere-turn per meter = 4π × 10⁻³ Oersteds
In practice, all magnetized materials retain some magnetization even when magnetizing force reduces to zero—this effect is known as ‘remanence,’ leading to different responses on decreasing versus increasing magnetizing force—a phenomenon termed ‘hysteresis loop.’
The hysteresis loop illustrates a material’s true B-H response, with its slope, saturation level, and size dependent on material type and other factors.
This concept can be further illustrated through 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 400 Hz 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 |
Hysteresis Loss
The B-H curve illustrates a phenomenon known as hysteresis, where the magnetization of the core material does not immediately follow the magnetizing force. This lag results in energy losses termed hysteresis loss. Materials with larger hysteresis loops experience greater losses, as these losses are represented by the area enclosed within the B-H hysteresis loop. Consequently, transformer cores are constructed using materials that exhibit low hysteresis loss to maximize efficiency.
Eddy Current Loss
Eddy currents, also referred to as Foucault currents, are loops of electrical current induced within the core material by the alternating magnetic flux. These currents generate resistive losses, leading to heating of the core, a phenomenon known as Eddy Current Loss. To reduce these losses, transformer cores are typically made from laminated sheets or ferrite materials, which limit the paths available for these currents.
Transformer Equivalent Circuit
An ideal transformer with one primary winding and two secondary windings can be represented as follows:
Such a transformer is characterized by:
- Absence of losses
- Perfect coupling between all windings
- Infinite open circuit impedance (no input current when secondaries are open-circuited)
- Infinite insulation between windings
In reality, transformers deviate from this ideal model due to various non-ideal characteristics. The equivalent circuits of transformers incorporate these aspects:
- Winding Resistances
- Capacitances
- Core Losses
- Magnetizing Inductance
- Leakage Inductances
These parameters help in predicting transformer performance and deviations from the ideal model. Many of these characteristics can be depicted in a transformer’s equivalent circuit:
Where:
- R1,R2,R3R1,R2,R3 represent the resistance of the winding wire.
- C1,C2,C3C1,C2,C3 represent the capacitance between the windings.
- RpRp accounts for losses due to eddy currents and hysteresis, known as core loss. These are real power losses measurable through an open-circuit power test. With no load current, I²R copper loss in the energized winding is minimal, making most measured watts attributable to the core.
- LpLp represents impedance due to magnetizing current. This current generates the magnetizing force HH, used in B-H loop diagrams. Note that this current might not be a simple sine wave; it can be distorted if operating in the non-linear region of the B-H curve, common in line-frequency laminate-type transformers.
- L1,L2,L3L1,L2,L3 denote each winding’s leakage inductance.
Conclusions
The equivalent circuit of a transformer accurately reflects the real properties of its magnetic circuit, including both core and windings. Thus, it can be reliably used to understand and predict a transformer’s electrical performance across various scenarios. Understanding these fundamental principles and practical considerations equips engineers to design, test, and apply transformers effectively in diverse applications.
