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Consider how electricity gets to your home. Generators produce large voltages and currents at a power plant. The problem: getting the electricity from the plant to the homes, businesses, and other facilities that need it. This process involves the use of long wire transmission lines. Transformers are also required to step the voltages up or down. As another example, consider a radio broadcast or communications station. The transmitter produces high-frequency ac. The problem is getting the power to be radiated by
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the antenna, located some distance from the transmitter. This involves the use of an RF transmission line. The most common type is coaxial cable. Two-wire line is also sometimes used. At ultrahigh and microwave frequencies, another kind of transmission line, known as a waveguide, is often employed.
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Loss: The Less, The Better! The overriding concern in any power transmission system is minimizing the loss. Power wastage occurs almost entirely as heat in the transmission line conductors and dielectric, and in objects near the line. Some loss can take the form of unwanted electromagnetic radiation from the line. Loss also occurs in transformers. Power loss in an electrical system is analogous to the loss of usable work produced by friction in a mechanical system. The less of it, the better! In an ideal power transmission system, all of the power is VA power; that is, it is in the form of ac in the conductors and an alternating voltage between them. It is undesirable to have power in a transmission line or transformer exist in the form of true power, because that translates into either heat loss, or radiation loss, or both. The place for true power dissipation or radiation is in the load, such as electrical appliances or radio antennas. Power Measurement in a Transmission Line In an ac transmission line, power is measured by placing an ac voltmeter between the conductors, and an ac ammeter in series with one of the conductors (Fig. 17-9). Then the power P (in watts) is equal to the product of the rms voltage E (in volts) and the rms current I (in amperes). This technique can be used in any transmission line. But this is not necessarily an indication of the true power dissipated by the load at the end of the line. Recall that any transmission line has a characteristic impedance. This value, Zo, depends on the diameters of the line conductors, the spacing between the conductors, and the type of dielectric material that separates the conductors. If the load is a pure resistance R containing no reactance, and if R = Zo, then the power indicated by the voltmeter/ammeter scheme will be the same as the true power dissipated by the load provided that the voltmeter and ammeter are placed at the load end of the transmission line.
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17-9 Power measurement in a transmission line. Ideally, the voltage and
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the current should be measured at the same physical point on the line.
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If the load is a pure resistance but it differs from the characteristic impedance of the line, then the voltmeter and ammeter will not give an indication of the true power. Also, if there is any reactance in the load, the voltmeter/ammeter method will not be accurate, even if the resistive component happens to be the same as the characteristic impedance of the line. The physics of this is rather complicated, and we won t get into the details here. But you should remember that it is optimum for the impedance of a load to be a pure resistance R, such that R = Zo. When this is not the case, an impedance mismatch is said to exist. Small impedance mismatches can often be tolerated in power transmission systems. But this is not always the case. In very high frequency (VHF), ultrahigh frequency (UHF), and microwave radio transmitting systems, even a small impedance mismatch between the load and the line can cause excessive power losses in the line. An impedance mismatch can usually be corrected by means of a matching transformer between a transmission line and the load, and/or the deliberate addition of reactance at the load end of the line to cancel out any existing load reactance.
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Loss in a Mismatched Line When a transmission line is terminated in a resistance R = Zo, then the current and the voltage are constant all along the line, provided the line has no loss. The ratio of the voltage to the current, E/I, is equal to R and also equal to Zo. But this is an idealized case. No line is completely lossless. In a real-world transmission line, the current and voltage gradually decrease as a signal makes its way from the source to the load. But if the load is a pure resistance equal to the characteristic impedance of the line, the current and voltage remain in the same ratio at all points along the line (Fig. 17-10). Standing Waves If the load is not perfectly matched to the line, the current and voltage vary in a complicated way along the length of the line. In some places, the current is high; in other places it is low. The max-
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