transformer

transformer



A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled wires. A changing current in the first circuit (the primary) creates a changing magnetic field; in turn, this magnetic field induces a changing voltage in the second circuit (the secondary). By adding a load to the secondary circuit, one can make current flow in the transformer, thus transferring energy from one circuit to the other.

The secondary induced voltage VS is scaled from the primary VP by a factor ideally equal to the ratio of the number of turns of wire in their respective windings:


By appropriate selection of the numbers of turns, a transformer thus allows an alternating voltage to be stepped up — by making NS more than NP — or stepped down, by making it less.

A key application of transformers is to reduce the current before transmitting electrical energy over long distances through wires. Most wires have resistance and so dissipate electrical energy at a rate proportional to the square of the current through the wire. By transforming electrical power to a high-voltage, and therefore low-current form for transmission and back again afterwards, transformers enable the economic transmission of power over long distances. Consequently, transformers have shaped the electricity supply industry, permitting generation to be located remotely from points of demand.[1] All but a fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer.[2]

Transformers are some of the most efficient electrical 'machines',[3] with some large units able to transfer 99.75% of their input power to their output.[4] Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge gigavolt-ampere-rated units used to interconnect portions of national power grids. All operate with the same basic principles, though a variety of designs exist to perform specialized roles throughout home and industry.


Basic principles

The transformer is based on two principles: first, that an electric current can produce a magnetic field (electromagnetism) and, second, that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). By changing the current in the primary coil, one changes the strength of its magnetic field; since the secondary coil is wrapped around the same magnetic field, a voltage is induced across the secondary.

A simplified transformer design is shown in Figure 2. A current passing through the primary coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very high magnetic permeability, such as iron; this ensures that most of the magnetic field lines produced by the primary current are within the iron and pass through the secondary coil as well as the primary coil.

Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that


where VS is the instantaneous voltage, NS is the number of turns in the secondary coil and Φ equals the total magnetic flux through one turn of the coil. If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic field strength B and the area A through which it cuts. The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field varies with time according to the excitation of the primary.

Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer,[5] the instantaneous voltage across the primary winding equals


Taking the ratio of the two equations for VS and VP gives the basic equation[6] for stepping up or stepping down the voltage


Ideal power equation

If the secondary coil is attached to a load that allows current to flow, electrical power is transmitted from the primary circuit to the secondary circuit. Ideally, the transformer is perfectly efficient; all the incoming energy is transformed from the primary circuit to the magnetic field and thence to the secondary circuit. If this condition is met, the incoming electric power must equal the outgoing power
Pincoming = IPVP = Poutgoing = ISVS

giving the ideal transformer equation


Thus, if the voltage is stepped up (VS > VP), then the current is stepped down (IS < IP) by the same factor. In practice, most transformers are very efficient (see below), so that this formula is a good approximation.

Technical discussion

The simplified description above avoids several complicating factors, in particular the primary current required to establish a magnetic field in the core, and the contribution to the field due to current in the secondary circuit.

Models of an ideal transformer typically assume a core of negligible reluctance with two windings of zero resistance.[7] When a voltage is applied to the primary winding, a small current flows, driving flux around the magnetic circuit of the core.[7]. The current required to create the flux is termed the magnetising current; since the ideal core has been assumed to have near-zero reluctance, the magnetising current is negligible, although a presence is still required to create the magnetic field.

The changing magnetic field induces an electromotive force (EMF) across each winding.[8] Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages VP and VS measured at the terminals of the transformer, are equal to the corresponding EMFs. The primary EMF, acting as it does in opposition to the primary voltage, is sometimes termed the "back EMF".[9] This is due to the lenz's law which states that the induction of EMF would always be such that it will oppose development of any such change in magnetic field.

Practical considerations

The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings.[10] Such flux is termed leakage flux, and manifests itself as self-inductance in series with the mutually coupled transformer windings.[9] Leakage results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. It is not itself directly a source of power loss, but results in poorer voltage regulation, causing the secondary voltage to fail to be directly proportional to the primary, particularly under heavy load.[10] Distribution transformers are therefore normally designed to have very low leakage inductance.

However, in some applications, leakage can be a desirable property, and long magnetic paths, air gaps, or magnetic bypass shunts may be deliberately introduced to a transformer's design to limit the short-circuit current it will supply.[9] Leaky transformers may be used to supply loads that exhibit negative resistance, such as electric arcs, mercury vapor lamps, and neon signs; or for safely handling loads that become periodically short-circuited such as electric arc welders.[11] Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers that have a DC component added.

Effect of frequency

The time-derivative term in Faraday's Law shows that the flux in the core is the integral of the applied voltage.[12] An ideal transformer would, at least hypothetically, work under direct-current excitation, with the core flux increasing linearly with time.[13] In practice, the flux would rise very rapidly to the point where magnetic saturation of the core occurred, causing a huge increase in the magnetising current and overheating the transformer. All practical transformers must therefore operate under alternating (or pulsed) current conditions.[13]

The EMF of a transformer at a given flux density increases with frequency, an effect predicted by the universal transformer EMF equation.[7] By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation, and fewer turns are needed to achieve the same impedance. However properties such as core loss and conductor skin effect also increase with frequency. Aircraft and military equipment traditionally employ 400 Hz power supplies which are less efficient but this is more than offset by the reduction in core and winding weight.[14]

In general, operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetising current. At a frequency lower than the design value, with the rated voltage applied, the magnetising current may increase to an excessive level. Operation of a transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers may need to be equipped with "volts per hertz" over-excitation relays to protect the transformer from overvoltage at higher than rated frequency.

Knowledge of natural frequencies of transformer windings is of importance for the determination of the transient response of the windings to impulse and switching surge voltages.

Energy losses

An ideal transformer would have no energy losses, and would therefore be 100% efficient. Despite the transformer being amongst the most efficient of electrical machines, with experimental models using superconducting windings achieving efficiencies of 99.85%,[15] energy is dissipated in the windings, core, and surrounding structures. Larger transformers are generally more efficient, and those rated for electricity distribution usually perform better than 95%.[16] A small transformer, such as a plug-in "power brick" used for low-power consumer electronics, may be no more than 85% efficient; although individual power loss is small, the aggregate losses from the very large number of such devices is coming under increased scrutiny.[17]

Transformer losses are attributable to several causes and may be differentiated between those originating in the windings, sometimes termed copper loss, and those arising from the magnetic circuit, sometimes termed iron loss. The losses vary with load current, and may furthermore be expressed as "no-load" or "full-load" loss, or at an intermediate loading. Winding resistance dominates load losses, whereas hysteresis and eddy currents losses contribute to over 99% of the no-load loss. The no-load loss can be significant, meaning that even an idle transformer constitutes a drain on an electrical supply, and lending impetus to development of low-loss transformers (also see energy efficient transformer).[18]