Ideal Transformer

A transformer is a device in which two circuits are coupled by a magnetic field that is linked to both. There is no conductive connection between the circuits, which may be at arbitrary constant potentials. Only changes in one circuit affect the other. The circuits often carry at least approximately sinusoidal currents, and the effect of the transformer is to change the voltages, while transferring power with little loss. Sinusoidal excitation is not necessary, and transformers may handle arbitrary signals, in which the action can be considered as a transformation of impedances. The magnetic field coupling the circuits can be in air, but is usually in a ferromagnetic material, the core, in which the field can be thousands of times greater than it would be in air, making the transformer efficient and small. The transformer is an honorary electrical "machine" in which the flux changes occur by variation in currents with time, instead of by motion.

Most transformers with iron cores can be considered as ideal when you use them. An ideal transformer has no losses, an aim that is closely attained in practice, so the energy transfer from the primary circuit to the secondary circuit is perfect. The diagram represents such a transformer, showing the core with magnetic flux φ, the primary winding of N₁ turns, and the secondary winding of N₂ turns. The reference directions for the voltages and currents at the terminals are shown. All of these quantities are to be considered as phasor amplitudes, varying sinusoidally with time. Note the dots at one or the other of the terminals of each winding. Currents entering the dotted terminals produce flux in the same direction, the direction shown. The current and voltage ratios are equal to the turns ratio. This means that the power factor (cosine of the phase angle), and the power, are the same at input (primary) and output (secondary). These things you probably already know, and we will not explore their consequences further.

The diagram shows the usual schematic way to represent a transformer. In an actual transformer, the windings are wound on top of each other, not on separate legs, to reduce leakage flux. In the usual shell-type transformer, both primary and secondary are on one leg, and are surrounded by the core. A core-type transformer has windings covering the core legs.

In order to design a transformer, or to examine in more detail how it departs from ideality, it is necessary to understand how a transformer works, not just how to express its terminal relations in an approximate way. It is also important to know how the properties of the iron core affect the performance of the transformer. A real transformer becomes hot because of losses, and the ouput voltage may vary with load even when the primary voltage is held constant.

The mutual flux φ is the means of transfer of energy from primary to secondary, and links both windings. In an ideal transformer, this flux requires negligibly small ampere-turns to produce it, so the net ampere-turns, primary plus secondary, is about zero. When a current is drawn from the secondary in the positive direction, ampere-turns decrease substantially. This must be matched by an equal increase in primary ampere-turns, which is caused by an increase in the current entering the primary in the positive direction. In this way, the back-emf of the primary (the voltage induced in it by the flux φ) equals the voltage applied to the primary, as it must. This fundamental explanation of the operation of a transformer must be clearly understood before proceeding further.

Key point:How a transformer works