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Power measurement in a transmission line
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In a transmission line, power is measured by means of a voltmeter between the conductors, and an ammeter in series with one of the conductors (Fig. 17-9). Then the power, P (in watts) is equal to the product of the voltage E (in volts) and the current I (in amperes). This technique can be used in any transmission line, be it for 60-Hz utility service, or in a radio transmitting station.
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17-9 Power measurement in a transmission line.
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But is this indication of power the same as the power actually dissipated by the load at the end of the line Not necessarily. Recall, from the discussion of impedance, that any transmission line has a characteristic impedance. This value, Zo, depends on the size of the line conductors, the spacing between the conductors, and the type of dielectric material that separates the conductors. For a coaxial cable, Zo can be anywhere from about 50 to 150 . For a parallel-wire line, it can range from about 75 to 600 . 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. The voltmeter and ammeter must be placed at the load end of the transmission line. If the load is a pure resistance R, and R < Zo or R > Zo, 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. The physics of this is rather sophisticated, and a thorough treatment of it is beyond the scope of this course. But you should remember that it is always desirable to have the load impedance be a pure resistance, a complex value of R j0, where R Zo. Small discrepancies, in the form of a slightly larger or smaller resistance, or a small reactance, can sometimes be tolerated. But in very-high-frequency (VHF), ultra-high-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.
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Power transmission 317 An impedance mismatch can usually be corrected by means of matching transformers and/or reactances that cancel out any load reactance. This is discussed in the next chapter.
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Loss in a mismatched line
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When a transmission line is terminated in a resistance R Zo, then the current and the voltage are constant all along the line, if the line is perfectly lossless. The ratio of the voltage to the current, E/I, is equal to R and also equal to Zo. Actually, this is an idealized case; no line is completely without loss. Therefore, as a signal goes along the line from a source to a load, the current and voltage gradually decrease. But they are always in same ratio (Fig. 17-10).
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17-10 In a matched line, E/I is constant, although both E and I decrease with increasing distance from the source.
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Standing waves
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If the load is not 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 maxima and minima are called loops and nodes respectively. At a current loop, the voltage is minimum (a voltage node), and at a current node, the voltage is maximum (a voltage loop). Loops and nodes make it impossible to measure power by the voltmeter/ammeter method, because the current and voltage are not in constant proportion. The loops and nodes, if graphed, form wavelike patterns along the length of the line. These patterns remain fixed over time. They are therefore known as standing waves they just stand there.
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