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Magnetizing current is in phase with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits. With open-circuited secondary winding, magnetizing branch current I 0 equals transformer no-load current. The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a number of approximations. This introduces error but allows combination of primary and referred secondary resistances and reactances by simple summation as two series impedances.

Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: open-circuit test , short-circuit test , winding resistance test, and transformer ratio test. A dot convention is often used in transformer circuit diagrams, nameplates or terminal markings to define the relative polarity of transformer windings. Three-phase transformers used in electric power systems will have a nameplate that indicate the phase relationships between their terminals.

This may be in the form of a phasor diagram, or using an alpha-numeric code to show the type of internal connection wye or delta for each winding. The EMF of a transformer at a given flux increases with frequency. However, properties such as core loss and conductor skin effect also increase with frequency.

Consequently, the transformers used to step-down the high overhead line voltages were much larger and heavier for the same power rating than those required for the higher frequencies. Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current.

At a lower frequency, the magnetizing current will increase.

Operation of a large transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. Transformers may require protective relays to protect the transformer from overvoltage at higher than rated frequency. One example is in traction transformers used for electric multiple unit and high-speed train service operating across regions with different electrical standards. At much higher frequencies the transformer core size required drops dramatically: a physically small transformer can handle power levels that would require a massive iron core at mains frequency.

The development of switching power semiconductor devices made switch-mode power supplies viable, to generate a high frequency, then change the voltage level with a small transformer. Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning. Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity.

Practical Transformer Handbook For Electronics Radio And Communications Engineers

The efficiency of typical distribution transformers is between about 98 and 99 percent. As transformer losses vary with load, it is often useful to tabulate no-load loss, full-load loss, half-load loss, and so on. Hysteresis and eddy current losses are constant at all load levels and dominate at no load, while winding loss increases as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply.

Designing energy efficient transformers for lower loss requires a larger core, good-quality silicon steel , or even amorphous steel for the core and thicker wire, increasing initial cost. The choice of construction represents a trade-off between initial cost and operating cost. Closed-core transformers are constructed in 'core form' or 'shell form'. When windings surround the core, the transformer is core form; when windings are surrounded by the core, the transformer is shell form.

At higher voltage and power ratings, shell form transformers tend to be more prevalent. Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel. Each lamination is insulated from its neighbors by a thin non-conducting layer of insulation.

The effect of laminations is to confine eddy currents to highly elliptical paths that enclose little flux, and so reduce their magnitude. Thinner laminations reduce losses, [27] but are more laborious and expensive to construct. One common design of laminated core is made from interleaved stacks of E-shaped steel sheets capped with I-shaped pieces, leading to its name of 'E-I transformer'. The cut-core or C-core type is made by winding a steel strip around a rectangular form and then bonding the layers together.

It is then cut in two, forming two C shapes, and the core assembled by binding the two C halves together with a steel strap. A steel core's remanence means that it retains a static magnetic field when power is removed. When power is then reapplied, the residual field will cause a high inrush current until the effect of the remaining magnetism is reduced, usually after a few cycles of the applied AC waveform. On transformers connected to long, overhead power transmission lines, induced currents due to geomagnetic disturbances during solar storms can cause saturation of the core and operation of transformer protection devices.

Distribution transformers can achieve low no-load losses by using cores made with low-loss high-permeability silicon steel or amorphous non-crystalline metal alloy. The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load.


Powdered iron cores are used in circuits such as switch-mode power supplies that operate above mains frequencies and up to a few tens of kilohertz. These materials combine high magnetic permeability with high bulk electrical resistivity. For frequencies extending beyond the VHF band , cores made from non-conductive magnetic ceramic materials called ferrites are common.

Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of silicon steel or permalloy wound into a coil, powdered iron, or ferrite. The closed ring shape eliminates air gaps inherent in the construction of an E-I core. The primary and secondary coils are often wound concentrically to cover the entire surface of the core.

This minimizes the length of wire needed and provides screening to minimize the core's magnetic field from generating electromagnetic interference. Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level. Other advantages compared to E-I types, include smaller size about half , lower weight about half , less mechanical hum making them superior in audio amplifiers , lower exterior magnetic field about one tenth , low off-load losses making them more efficient in standby circuits , single-bolt mounting, and greater choice of shapes.

The main disadvantages are higher cost and limited power capacity see Classification parameters below. Because of the lack of a residual gap in the magnetic path, toroidal transformers also tend to exhibit higher inrush current, compared to laminated E-I types. Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of inductive components. A drawback of toroidal transformer construction is the higher labor cost of winding.

This is because it is necessary to pass the entire length of a coil winding through the core aperture each time a single turn is added to the coil. As a consequence, toroidal transformers rated more than a few kVA are uncommon. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings.

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A transformer can be produced by placing the windings near each other, an arrangement termed an "air-core" transformer. An air-core transformer eliminates loss due to hysteresis in the core material. Air-core transformers are unsuitable for use in power distribution, [12] but are frequently employed in radio-frequency applications. The electrical conductor used for the windings depends upon the application, but in all cases the individual turns must be electrically insulated from each other to ensure that the current travels throughout every turn.

For small transformers, in which currents are low and the potential difference between adjacent turns is small, the coils are often wound from enamelled magnet wire. Larger power transformers may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of pressboard. High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided Litz wire to minimize the skin-effect and proximity effect losses.

The transposition equalizes the current flowing in each strand of the conductor, and reduces eddy current losses in the winding itself. The stranded conductor is also more flexible than a solid conductor of similar size, aiding manufacture. The windings of signal transformers minimize leakage inductance and stray capacitance to improve high-frequency response.

Coils are split into sections, and those sections interleaved between the sections of the other winding.

Practical Transformer Handbook

Power-frequency transformers may have taps at intermediate points on the winding, usually on the higher voltage winding side, for voltage adjustment. Taps may be manually reconnected, or a manual or automatic switch may be provided for changing taps. Automatic on-load tap changers are used in electric power transmission or distribution, on equipment such as arc furnace transformers, or for automatic voltage regulators for sensitive loads. Audio-frequency transformers, used for the distribution of audio to public address loudspeakers, have taps to allow adjustment of impedance to each speaker.

A center-tapped transformer is often used in the output stage of an audio power amplifier in a push-pull circuit. Modulation transformers in AM transmitters are very similar. Small dry-type and liquid-immersed transformers are often self-cooled by natural convection and radiation heat dissipation. As power ratings increase, transformers are often cooled by forced-air cooling, forced-oil cooling, water-cooling, or combinations of these. The mineral oil and paper insulation system has been extensively studied and used for more than years.

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Building regulations in many jurisdictions require indoor liquid-filled transformers to either use dielectric fluids that are less flammable than oil, or be installed in fire-resistant rooms. The tank of liquid filled transformers often has radiators through which the liquid coolant circulates by natural convection or fins. Some large transformers employ electric fans for forced-air cooling, pumps for forced-liquid cooling, or have heat exchangers for water-cooling.

Polychlorinated biphenyls have properties that once favored their use as a dielectric coolant , though concerns over their environmental persistence led to a widespread ban on their use. Some transformers, instead of being liquid-filled, have their windings enclosed in sealed, pressurized tanks and cooled by nitrogen or sulfur hexafluoride gas.

Insulation must be provided between the individual turns of the windings, between the windings, between windings and core, and at the terminals of the winding.