barcode in vb.net 2010 Transformers and Impedance Matching in Software

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298 Transformers and Impedance Matching
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18-11 A quarter-wave
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matching section of transmission line. The input impedance is Rin, the output impedance is Rout, and the characteristic impedance of the line is Zo.
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These equations are valid at the frequency fo for which the line length measures 1 4 wavelength. Sometimes, the word wavelength is replaced by the lowercase Greek letter lambda ( ), so you will occasionally see the length of a quarter-wave section denoted as (1 4) or 0.25 . Neglecting line losses, the preceding relations hold at all odd harmonics of fo, that is, at 3fo, 5fo, 7fo, and so on. At other frequencies, a quarter-wave section of line does not act as a transformer. Instead, it behaves in a complex manner that is beyond the scope of this discussion. Quarter-wave transmission-line transformers are most often used in antenna systems, especially at the higher frequencies, where their dimensions become practical. A quarter-wave matching section should be made using unbalanced line if the load is unbalanced, and balanced line if the load is balanced. A disadvantage of quarter-wave sections is the fact that they work only at specific frequencies. But this is often offset by the ease with which they are constructed, if radio equipment is to be used at only one frequency, or at odd-harmonic frequencies.
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Problem 18-5 Suppose an antenna has a purely resistive impedance of 100 . It is connected to a 1 4-wave section of 75- coaxial cable. What is the impedance at the input end of the section Use the formula from above:
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R in = Z o2/R out = 752/100 = 5625/100 = 56
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Problem 18-6 Consider an antenna known to have a purely resistive impedance of 600 . You want to match it to the output of a radio transmitter designed to work into a 50.0- pure resistance. What is the characteristic impedance needed for a quarter-wave matching section Use this formula:
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Z 2 = R inR out = 600 50 = 30,000
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Quiz
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Therefore: Zo = (30,000)1/2 = 173 It may be difficult to find a commercially manufactured transmission line that has this particular characteristic impedance. Prefabricated lines come in standard Zo values, and a perfect match might not be obtainable. In that case, the closest obtainable Zo should be used. In this case, it would probably be 150 . If nothing is available anywhere near the characteristic impedance needed for a quarter-wave matching section, then a coil-type transformer can be used instead.
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What about Reactance Things are simple when there is no reactance in an ac circuit using transformers. But often, especially in RF antenna systems, pure resistance doesn t occur naturally. It has to be obtained by using inductors and/or capacitors to cancel the reactance out. The presence of reactance in a load makes a perfect match impossible with an impedance-matching transformer alone. Recall that inductive and capacitive reactances are opposite in effect, and that their magnitudes can vary. If a load presents a complex impedance R + jX, it is possible to cancel the reactance X by deliberately introducing an equal and opposite reactance X. This can be, and often is, done by connecting an inductor or capacitor in series with a load that contains reactance as well as resistance. The result is a pure resistance with a value equal to (R + jX ) jX, or simply R. When wireless communications is contemplated over a wide band of frequencies, adjustable impedance-matching and reactance-canceling networks can be placed between the transmitter and the antenna system. Such a device is called a transmatch or an antenna tuner. These devices not only match the resistive portions of the transmitter and load impedances, but they can tune out reactances in the load. Transmatches are popular among amateur radio operators, who use equipment capable of operation from less than 2 MHz up to the highest known radio frequencies.
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