### Power Transformers

Any transformer used in the 60-Hz utility line, intended to provide a certain rms ac voltage for the operation of electrical circuits, is a power transformer. Power transformers exist in a vast range of physical sizes, from smaller than a tennis ball to as big as a room.

#### At the Generating Plant

The largest transformers are employed at the places where electricity is generated. Not surprisingly, high-energy power plants have bigger transformers that develop higher voltages than low-energy, local power plants. These transformers must be able to handle high voltages and large currents simultaneously. When electrical energy must be sent over long distances, extremely high voltages are used. This is because, for a given amount of power ultimately dissipated by the loads, the current is lower when the voltage is higher. Lower current translates into reduced loss in the transmission line. Recall the formula P = EI, where P is the power (in watts), E is the voltage (in volts), and I is the current (in amperes). If you can make the voltage 10 times larger, for a given power level, then the current is reduced to 1⁄ 10 as much. The ohmic losses in the wires are proportional to the square of the current. Remember that P = I 2R, where P is the power (in watts), I is the current (in amperes), and R is the resistance (in ohms). Engineers can’t do much about the wire resistance or the power consumed by the loads, but they can adjust the voltage, and thereby the current. Suppose the voltage in a power transmission line is increased by a factor of 10, and the load at the end of the line draws constant power. This increase in the voltage reduces the current to 1⁄ 10 of its previous value. As a result, the ohmic loss is cut to (1⁄ 10)2, or 1⁄ 100, of its previous amount. That’s a major improvement in the efficiency of the transmission line, at least in terms of the loss caused by the resistance in the wires—and it is the reason why regional power plants have massive transformers capable of generating hundreds of thousands of volts.

#### Along the Line

At A, an outlet for three-phase, 234-V rms utility ac. At B, a conventional single-phase utility outlet for 117-V rms utility ac.
Extreme voltage is good for high-tension power transmission, but it’s certainly of no use to an average consumer. The wiring in a high-tension system must be done using precautions to prevent arcing (sparking) and short circuits. Personnel must be kept at least several meters away from the wires. Can you imagine trying to use an appliance, say a home computer, by plugging it into a 500,000-V rms electrical outlet? Medium-voltage power lines branch out from the major lines, and step-down transformers are used at the branch points. These lines fan out to still lower-voltage lines, and step-down transformers are employed at these points, too. Each transformer must have windings heavy enough to withstand the product P = EI, the amount of VA power delivered to all the subscribers served by that transformer, at periods of peak demand. Sometimes, such as during a heat wave, the demand for electricity rises above the normal peak level. This loads down the circuit to the point that the voltage drops several percent. This is called a brownout. If consumption rises further still, a dangerous current load is placed on one or more intermediate power transformers. Circuit breakers in the transformers protect them from destruction by opening the circuit. Then there is a temporary blackout. At individual homes and buildings, transformers step the voltage down to either 234 V rms or 117 V rms. Usually, 234-V rms electricity is provided in the form of three sine waves, called phases, each separated by 120°, and each appearing at one of the three slots in the outlet (above figure A). This voltage is commonly employed with heavy appliances, such as the kitchen oven/stove (if they are electric), heating (if it is electric), and the laundry washer and dryer. A 117-V rms outlet supplies just one phase, appearing between two of the three slots in the outlet. The third opening in the outlet leads to an earth ground (above figure B).

#### In Electronic Devices

The smallest power transformers are found in electronic equipment such as television sets, ham radios, and home computers. Most solid-state devices use low voltages, ranging from about 5 V up to perhaps 50 V. This equipment needs step-down power transformers in its power supplies. Solid-state equipment usually (but not always) consumes relatively little power, so the transformers are usually not very bulky. The exception is high-powered AF or RF amplifiers, whose transistors can demand more than 1000 W (1 kW) in some cases. At 12 V, this translates to a current demand of 90 A or more. Television sets have cathode-ray tubes that need several hundred volts. This is derived by using a step-up transformer in the power supply. Such transformers don’t have to supply a lot of current, though, so they are not very big or heavy. Another type of device that needs rather high voltage is a ham-radio amplifier with vacuum tubes. Such an amplifier requires from 2 kV to 5 kV. Any voltage higher than about 12 V should be treated with respect. Warning: The voltages in televisions and ham radios can present an electrocution hazard, even after the equipment has been switched off. Do not try to service such equipment unless you are trained to do so!

#### At Audio Frequencies

At A, a utility transformer E core, showing both sections. At B, the shell winding method. At C, the core winding method.
Transformers for use at AF are similar to those employed for 60-Hz electricity. The differences are that the frequency is somewhat higher (up to 20 kHz), and that audio signals exist in a band of frequencies (20 Hz to 20 kHz) rather than at only one frequency. Most AF transformers are constructed like miniature utility transformers. They have laminated E cores with primary and secondary windings wound around the crossbars, as shown in above figure. Audio transformers can be either the step-up or the step-down type. However, rather than being made to produce a specific voltage, AF transformers are designed to match impedances. Audio circuits, and in fact all electronic circuits that handle sine-wave or complex-wave signals, exhibit impedance at the input and output. The load has a certain impedance; a source has another impedance. Good audio design strives to minimize the reactance in the circuitry, so that the absolute-value impedance Z is close to the resistance R. This means that X must be zero or nearly zero. In the following discussion of impedance-matching transformers, for both AF and RF applications, assume that the reactance is zero, so the impedance is purely resistive with Z = R + j 0.