Transformers

Type of physical science: Classical physics

Field of study: Electromagnetism

A transformer is an electrical device that uses electromagnetic induction to convert the voltage in a circuit either to a higher or lower value. Their wide variety of applications includes power distribution systems, appliances, and toys.

Overview

Transformers serve the useful purpose of conveying electrical power between two circuits without the circuits having to be directly connected. Simultaneously, the transformers can convert the voltage level of this power to a higher or lower value (or simply at a constant value). Transformers operate on the principles of electromagnetic induction, discovered by Michael Faraday in 1831 at the Royal Institution in London. An electric current (flowing in a wire) always produces a magnetic field that surrounds the current; a current whose magnitude changes with time produces a magnetic field whose magnitude also changes with time.

Conversely, a changing magnetic field in the vicinity of a wire induces a voltage that causes a changing current to flow in the wire. (A constant magnetic field does not induce a constant voltage.)

In the case of transformers, at least two wires are involved. Each is usually formed into a coil of some form, and the two coils are placed close together, but not necessarily touching.

There is one primary coil, and one or more secondary coils; the coils are often called windings, and their wire loops are called turns. Placing a constant voltage (for example, using a battery) across the primary winding causes a current to begin to flow. Before this current reaches a steady value, it creates a magnetic field that is also growing in magnitude, which consequently induces a voltage in the secondary winding. Once the primary current reaches its steady value, so does the magnetic field, and the secondary voltage disappears. Therefore, the primary voltage is usually made to oscillate sinusoidally (that is, vary smoothly and periodically between two values). The resulting oscillations in primary current produce an oscillating magnetic field, which in turn induces an oscillating secondary voltage. Both the primary and secondary voltages (and the corresponding currents), as well as the magnetic field generated by the primary winding, oscillate at the same frequency. A simple relationship governs the operation of a transformer: The ratio of primary to secondary voltage equals the ratio of secondary to primary turns of wire. For example, if a voltage that varies sinusoidally between 100 volts and -100 volts is applied to the primary winding of a transformer with 400 primary turns and 100 secondary turns, the secondary voltage will be 25 volts.

The physical form of a transformer depends upon several factors, including the amount of inductive coupling required and the potential range of oscillating frequencies involved.

Generally, the coils are wound on an object called the core, which not only serves as physical support for the winding but also can help to contain the magnetic field. Certain magnetic materials serve this latter purpose quite well, notably the ferromagnetic compounds (for example, iron). The better the magnetic field is contained, the more complete the transfer of electrical power between the coils. In an ideal transformer, the magnetic field is completely contained in the core, allowing all the power to be transferred to the secondary circuit.

Realistically, however, four different phenomena prevent this from occurring. Both coils have some electrical resistance and therefore a small amount of power is lost as heat in the windings (referred to as copper losses). Second, some of the magnetic field generated by the primary current will be outside the core, where it cannot contribute to the induction in the secondary coil (referred to as inductive losses). Third, the core itself (usually an electrical conductor) will experience an induced voltage and, consequently, electric currents (called "eddy currents") will flow within the core. The electrical resistance of the core material then dissipates the energy of these internal currents as heat (referred to as eddy losses). Finally, the oscillating magnetic field in the core causes a reversing magnetization of the core material, which removes energy from the magnetic field (referred to as hysteresis losses). The manifestation of this loss is an additional warming of the core. Each of these four losses reduces the amount of power available in the secondary winding, typically by 3 to 5 percent.

Improvements in performance can be obtained by employing low-resistivity wire and by using the largest possible wire diameter to lower the electrical resistance further. The choice of core material depends largely on the range of oscillation frequencies of the current involved.

For example, iron compounds work well for high-power applications and low frequencies such as the 60 hertz (cycles per second) used by power companies for distributing electrical power; however, at radio frequencies (for example, 1,000,000 hertz), the hysteresis and eddy losses may be unacceptable. Generally, hollow ceramic or plastic forms (air cores) work well at these high frequencies. Improving technology has continued to make ferromagnetic cores perform better at higher frequencies, making it possible to employ their superior fieldcontainment properties.

In low-frequency applications, eddy losses are successfully reduced through the use of laminated iron cores. The core is divided into a number of thin layers (laminae) and separated by thin layers of electrical insulation, usually a baked enamel. This insulation prevents the flow of eddy currents between laminae and thus reduces the overall current in the core and the corresponding eddy losses. Dividing the core into even thinner laminae reduces the eddy losses significantly, but the enamel layers must maintain a minimum thickness to prevent electrical arcing, and the total core thickness can thus become too great for practical use.

At high frequencies, the capacitance between laminae can adversely affect the circuit in which the transformer is placed; therefore, laminated cores are avoided. Powdered ferromagnetic compounds, mixed with electrically insulating cement, have low eddy losses and good magnetic field containment at high frequencies but are more expensive to manufacture and somewhat less durable than iron cores (that is, the powdered cores are more brittle and subject to cracking).

In general, transformers are designed so that the core forms a closed loop, either as a simple torus or sometimes with more complex geometry. This reduces leakage of the magnetic field but makes construction of the transformer somewhat more complicated. It is important to keep the core path as short as possible to reduce eddy losses and magnetic field leakage.

Two common forms of cores are the shell, which consists of an E-shaped piece (often laminated), with both the primary and secondary coils wound on the short center section, and an I-shaped piece (also usually laminated), which is cemented to close the E-section. The result effectively gives two cores that share a common side (on which the coils are wound); however, because the I-section is separated by a thin layer of cement, the magnetic path is not completely closed and some leakage is inevitable. The ease of winding on the open E-section provides some compromise between performance and cost. A second form avoids the leakage problem by using two C-shaped laminated stacks with a separate winding on the middle section of each. The two stacks are joined by interleaving the laminae as the open sides of the C-sections are joined.

In cases where electrical isolation between two circuits is not required but a voltage change is needed, an autotransformer may be useful. This device uses the same principles of electromagnetic induction but employs only one winding, to the middle of which is connected a third wire. The primary winding is the entire coil, but the secondary is only that part of the winding between one end of the original coil and the third wire. This arrangement can result in substantial reduction in the total amount of wire needed (and also reduce the copper losses).

Applications

The most common and well-known use of transformers is in the power distribution system that provides electricity to homes, buildings, industry, and the like. Power is initially generated at a central plant in an oscillating form (alternating current), with a frequency of 60 hertz. The voltage is stepped up using transformers that have large secondary-to-primary turn ratios, resulting in electrical power with high voltage but relatively low current. Because the resistive losses in the distribution network are proportional to the square of the current, this approach reduces the loss of power during distribution to the users. An added advantage is that the distribution wires can be considerably smaller in diameter than if no transformers were used, since the reduced current requires smaller cross-sectional area in the conducting material of the wire. Power can be transmitted over many kilometers in this way with only minor loss because of resistance; however, the extremely high voltages necessitate the use of elevated transmission lines for safety.

Even with the small percentage of power lost because of hysteresis, eddy currents, and the like, these step-up transformers dissipate considerable heat and must be cooled by keeping them immersed in oil or by circulating cooling liquids through the cores to transport the heat to a radiator, where it is emitted into the air. Near the user's end of the network, a step-down transformer converts the power back to a lower-voltage (and higher-current) form that is suitable for use in homes and offices. Some industries require much higher voltages, and the corresponding step-down transformers at those locations can be designed with smaller turn ratios. In many networks, the wiring takes the form of a tree, with each major branch carrying power to a group of users in an area. Since the wires must now be brought lower to the ground for users to access them, the voltage levels must also be lowered for safety. A series of transformers is employed, each at one of the forks in the wiring network to step down the voltage for that branch. The network for a metropolitan community may contain hundreds of thousands of these intermediate step-down transformers, with a final voltage reduction occurring at a local transformer in each neighborhood, giving a typical level of approximately 110 volts.

While many appliances appear to use this form of electrical power directly, frequently they contain internal transformers that either step up or step down the voltage. For example, most solid-state electronic equipment operates at less than 10 volts. A step-down transformer can convert the 110 volts to 10 volts (and then a power conditioning circuit must convert the power to direct current). Circuits that require several different voltages can use a transformer with one primary and several secondary windings, each producing the desired voltage. Indeed, a single transformer often has some secondary windings that step up the voltage and some that step it down. This is the case with televisions and computers that use cathode-ray tubes as displays (requiring up to 25,000 volts), while employing low-voltage integrated circuits for the signal processing or computing actions.

A second routine use of transformers is in audio amplifiers, where the output signal must go to an audio speaker and produce sufficient sound volume level. The speaker also operates via electromagnetic induction: The input signal to the speaker is an electric current that creates a magnetic field in the speaker coils. The current changes in proportion to the intensity of the audio signal that is to be reproduced and causes the speaker's membrane (which has attached a small permanent magnet) to vibrate at a frequency and amplitude proportional to that of the audio signal. Good performance of the speaker requires a significant current in the speaker coils in order to generate a strong magnetic field. By inserting a step-down transformer between the audio circuit and the speaker, the output current to the speaker is made greater than it would be without the transformer.

In many circuits, the power being output to a second circuit can be maximized if the second circuit has a particular electrical resistance or can be made to appear effectively as though it has that resistance. This is called "impedance matching," and a transformer can be employed for this purpose. Impedance is analogous in alternating current circuits to resistance in circuits that use direct current. The relationship between current, voltage, and resistance is given by Ohm's law, which states that voltage equals current (measured in amperes) times resistance (measured in ohms). For example, if the first circuit has an output impedance of 100 ohms, then the second circuit (which receives the output power from the first) should be made to have, or appear to have, the same impedance. If the second circuit has an input impedance of 10 ohms and the first circuit outputs 100 volts at 200 ohms output impedance, then a transformer with 45 primary windings and 10 secondary windings will give 100 volts/4.5 = 22.2 volts at the second circuit. By Ohm's law, the second circuit will draw 22.2 volts/10 = 2.22 amperes of current.

Therefore, the secondary coil of the transformer delivers 49.3 volt-amperes; however, the input volt-amperes to the transformer must be nearly equal to the output, so the transformer must be drawing 49.3 volt-amperes. Since the first circuit outputs at 100 volts, it now sees an impedance of 100 volts/0.493 amperes = 202 ohms, which is approximately what was desired.

Context

Following Faraday's discovery of electromagnetic induction, a number of successful experiments demonstrated the feasibility of stepping-up and stepping-down voltages. In 1884, the first commercial transformers were operated by the Hungarian team of Max Deri, Otto Blathy (who introduced the term "transformer"), and Karl Zipernowsky. Their transformers, which had iron cores, were used in a simple power distribution system for lighting at an exposition in Budapest in 1885. In the United States, George Westinghouse purchased patent rights in 1886 on the invention of an induction coil system developed previously by Lucien Gaulard and Josiah Willard Gibbs. Under Westinghouse's encouragement, one of his engineers, William Stanley further developed the ideas of Gaulard and Gibbs, introducing the use of laminated and continuous cores. Westinghouse was the first to suggest the use of a shell core to ease the construction. His plant in Buffalo, New York, which began operation in November, 1886, was the first for distributing power using step-up and step-down transformers.

The capability to transmit electrical power over great distances made it possible to locate power-generation plants remotely from populated areas. This was particularly important for hydroelectric generation plants located on dams, sometimes far removed from metropolitan centers. Nuclear power plants must be located near bodies of water (for cooling purposes), which also are frequently rather distant from the users of the power.

Transformers will continue to serve a crucial role for electrical isolation. In many appliances, it would be possible to achieve the necessary low-voltage by simply using resistors to drop the voltage from the customary 110 volts to the desired value. This poses a hazard, though, because overheating of a resistor could result in a failure, placing the full 110 volts across parts of the low-voltage circuitry. Such a voltage level is life-threatening and so the use of "transformerless" power supplies in appliances is too dangerous. A step-down transformer also serves to isolate the high-voltage wires from the low-voltage circuits. Failure of a transformer in such a way as to cause high voltage to appear on the secondary side is far less likely than the dangerous failure of the resistor system.

Principal terms

ALTERNATING CURRENT: an electric current that smoothly and periodically changes direction in a circuit

CORE: internal material in a transformer that helps to contain the magnetic field

EDDY CURRENTS: electrical currents induced in a transformer's core by the changing magnetic field generated by the primary coil

ELECTROMAGNETIC INDUCTION: a phenomenon in which a changing magnetic field induces a changing voltage in a circuit; a changing voltage generates a changing magnetic field

Bibliography

Asimov, Isaac. UNDERSTANDING PHYSICS. Vol. 2. New York: Walker, 1966. This two-volume set treats both classical and modern physics with minimal mathematics. The explanations are lucid and witty. His examples are drawn from common experience and serve to illustrate the concepts quite effectively.

Borowitz, Sidney, and L. A. Bornstein. A CONTEMPORARY VIEW OF ELEMENTARY PHYSICS. New York: McGraw-Hill, 1968. An introductory physics text, this contains an excellent treatment of electromagnetic induction and some of the history of its discovery. A most appealing aspect of this book is that it allows the reader to see the mathematical descriptions of the physical phenomena without relying on calculus.

Feynman, Richard P., Robert B. Leighton, and Matthew Sands. THE FEYNMAN LECTURES ON PHYSICS. Vol. 2. Reading, Mass.: Addison-Wesley, 1963. These lectures challenged some of the brightest physics students at the California Institute of Technology, yet they have exceptional clarity and appeal for general audiences.

Effectively treats the approximate nature of physical laws. Gamow, George. MATTER, EARTH, AND SKY. Englewood Cliffs, N.J.: Prentice-Hall, 1965. Geared for freshman physics courses. Based on Gamow's experience in lecturing and writing for general audiences interested in science. Combines physics, chemistry, geology, and astronomy, including numerous helpful diagrams and some of the author's own cartoons.

Wilson, Mark J., ed. THE ARRL HANDBOOK FOR THE RADIO AMATEUR. 65th ed. Newington, Conn.: The American Radio Relay League, 1988. Intended as a reference source for amateur ("ham") radio operators, this remarkable book also quite successfully teaches about a wide variety of electrical components and circuits, requiring only a modest knowledge of electricity and mangnetism. Contains an extensive treatment of the theory and uses of transformers, along with numerous tables of design data.

Charges and Currents

Conductors and Resistors