# Transformers by Stan Gibilisco

Principle of the transformer

When two wires are near each other, and one of them carries a fluctuating current, a current will be induced in the other wire. This effect is known as electromagnetic induction. All ac transformers work according to the principle of electromagnetic induction. If the first wire carries sine-wave ac of a certain frequency, then the induced current will be sine-wave ac of the same frequency in the second wire.

The closer the two wires are to each other, the greater the induced current will be, for a given current in the first wire. If the wires are wound into coils and placed along a common axis (Fig. 18-1), the induced current will be greater than if the wires are straight and parallel. Even more coupling, or efficiency of induced-current transfer, is obtained if the two coils are wound one atop the other.

The first coil is called the primary winding, and the second coil is known as the secondary winding. These are often spoken of as simply the primary and secondary. The induced current creates a voltage across the secondary. In a step-down transformer, the secondary voltage is less than the primary voltage. In a step-up transformer, the secondary voltage is greater than the primary voltage. The primary voltage is abbreviated Epri, and the secondary voltage is abbreviated Esec. Unless otherwise stated, effective (rms) voltages are always specified.

The windings of a transformer have inductance because they are coils. The required inductances of the primary and secondary depend on the frequency of operation, and also on the resistive part of the impedance in the circuit. As the frequency increases, the needed inductance decreases. At high-resistive impedances, more inductance is generally needed than at low-resistive impedances.

Turns ratio

The turns ratio in a transformer is the ratio of the number of turns in the primary, Tpri, to the number of turns in the secondary, Tsec. This ratio is written Tpri:Tsec or Tpri/Tsec. In a transformer with excellent primary-to-secondary coupling, the following relationship always holds:

Epri/Esec = Tpri/Tsec

That is, the primary-to-secondary voltage ratio is always equal to the primary-to-secondary turns ratio (Fig. 18-2).

A step-down transformer always has a primary-to-secondary turns ratio greater than 1, and a step-up transformer has a primary-to-secondary turns ratio less than 1. Sometimes the secondary-to-primary turns ratio is given. This is the reciprocal of the primary-to-secondary turns ratio, written Tsec/Tpri. In a step-down unit, Tsec/Tpri < 1; in a step-up unit, Tsec/Tpri > 1.

When you hear someone say that such-and-such a transformer has a certain turns ratio, say 10:1, you need to be sure of which ratio is meant, Tpri/Tsec or Tsec/Tpri! If you get it wrong, you'll have the secondary voltage off by a factor of the square of the turns ratio. You might be thinking of 12 V when the engineer is talking about 1200 V. One way to get rid of doubt is to ask, "Step-up or step-down?"

Transformer cores

If a ferromagnetic substance such as iron, powdered iron, or ferrite is placed within the pair of coils, the extent of coupling is increased far above that possible with an air core. But this improvement in coupling takes place with a price; some energy is invariably lost as heat in the core. Also, ferromagnetic transformer cores limit the frequency at which the transformer will work well.

The schematic symbol for an air-core transformer consists of two inductor symbols back-to-back (Fig. 18-3A). If a ferromagnetic core is used, two parallel lines are added to the schematic symbol (Fig. 18-3B)

Transformer geometry

The shape of a transformer depends on the shape of its core. There are several different core geometries commonly used with transformers.

A common core for a power transformer is the E core, so named because it is shaped like the capital letter E. A bar, placed at the open end of the E, completes the core once the coils have been wound on the E-shaped section (Fig. 18-4A).

The primary and secondary windings can be placed on an E core in either of two ways.

The simpler winding method is to put both the primary and the secondary around the middle bar of the E (Fig. 18-4B). This is called the shell method of transformer winding. It provides maximum coupling between the windings. However, the shellwinding scheme results in a considerable capacitance between the primary and the secondary. This capacitance can sometimes be tolerated; sometimes it cannot. Another disadvantage of the shell geometry is that, when windings are placed one atop the other, the transformer cannot handle very much voltage.

Another winding method is the core method. In this scheme, the primary is placed at the bottom of the E section, and the secondary is placed at the top (Fig. 18-4C). The coupling occurs via magnetic flux in the core. The capacitance between the primary and secondary is much lower with this type of winding. Also, a core-wound transformer can handle higher voltages than the shell-wound transformer. Sometimes the center part of the E is left out of the core when this winding scheme is used.

Shell-wound and core-wound transformers are almost universally employed at 60 Hz. These configurations are also common at audio frequencies.

Stan Gibilisco is one of McGraw-Hill's most prolific and popular authors, specializing in electronics and science topics. His clear, reader-friendly writing style makes his science books accessible to a wide audience, and his background in research makes him an ideal editor for professional references and course materials. He is the author of The Encyclopedia of Electronics; The McGraw-Hill Encyclopedia of Personal Computing; and several titles in the popular Demystified library of home-schooling and self-teaching books. His published works have won numerous awards. The Encyclopedia of Electronics was chosen a "Best Reference Book of the 1980s" by the American Library Association, which also named his McGraw-Hill Encyclopedia of Personal Computing a "Best Reference of 1996." Stan Gibilisco maintains a Web site at www.sciencewriter.net.

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