barcode in vb.net 2010 In a matched line, the ratio of the voltage to the current (E/I ) is in Software

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17-10 In a matched line, the ratio of the voltage to the current (E/I ) is
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constant everywhere along the line, although the actual values of E and I decrease with increasing distance from the source.
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276 Power and Resonance in Alternating-Current Circuits
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ima 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). The current and voltage loops and nodes along a mismatched transmission line, if graphed as functions of the position on the line, form wavelike patterns that remain fixed over time. They just stand there. For this reason, they are called standing waves.
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Standing-Wave Loss At current loops, the loss in line conductors reaches a maximum. At voltage loops, the loss in the dielectric reaches a maximum. At current nodes, the loss in the conductors reaches a minimum. At voltage nodes, the loss in the dielectric reaches a minimum. It is tempting to suppose that everything would average out here, but it doesn t work that way! Overall, in a mismatched line, the line losses are greater than they are in a perfectly matched line. This extra line loss increases as the mismatch gets worse. Transmission-line mismatch loss, also called standing-wave loss, occurs in the form of heat dissipation. It is true power. Any true power that goes into heating up a transmission line is wasted, because it cannot be dissipated in the load. The greater the mismatch, the more severe the standing-wave loss becomes. The more loss a line has to begin with (that is, when it is perfectly matched), the more loss is caused by a given amount of mismatch. Standing-wave loss also increases as the frequency increases, if all other factors are held constant. This loss is the most significant, and the most harmful, in long lengths of transmission line, especially in RF practice at VHF, UHF, and microwave frequencies. Line Overheating A severe mismatch between the load and the transmission line can cause another problem: physical damage to, or destruction of, the line! A feed line might be able to handle a kilowatt (1 kW) of power when it is perfectly matched. But if a severe mismatch exists and you try to feed 1 kW into the line, the extra current at the current loops can heat the conductors to the point where the dielectric material melts and the line shorts out. It is also possible for the voltage at the voltage loops to cause arcing between the line conductors. This perforates and/or burns the dielectric, ruining the line. When an RF transmission line must be used with a mismatch, derating functions are required to determine how much power the line can safely handle. Manufacturers of prefabricated lines such as coaxial cable can supply you with this information.
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Resonance
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One of the most important phenomena in ac circuits, especially in RF engineering, is the property of resonance. This is a condition that occurs when capacitive and inductive reactance cancel each other out.
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Series Resonance Recall that capacitive reactance, XC, and inductive reactance, XL, can be equal in magnitude, although they are always opposite in effect. In any circuit containing an inductance and capacitance, there exists a frequency at which XL = XC. This condition constitutes resonance. In a simple LC circuit, there is only one such frequency. But in some circuits involving transmission lines or antennas,
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17-11 A series RLC circuit.
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there can be many such frequencies. The lowest frequency at which resonance occurs is called the resonant frequency, symbolized fo. Refer to the schematic diagram of Fig. 17-11. You should recognize this as a series RLC circuit. At some particular frequency, XL = XC. This is inevitable if L and C are finite and nonzero. This frequency is fo for the circuit. At fo, the effects of capacitive reactance and inductive reactance cancel out. The result is that the circuit appears as a pure resistance, with a value that is theoretically equal to R. If R = 0, that is, if the resistor is a short circuit, then the circuit is called a series LC circuit, and the impedance at resonance will be theoretically 0 + j 0. The circuit will offer no opposition to the flow of alternating current at the frequency fo. This condition is series resonance. In a practical series LC circuit, there is always a little bit of loss in the coil and capacitor, so the real part of the complex impedance is not exactly equal to 0 (although it can be extremely small).
Parallel Resonance Refer to the circuit diagram of Fig. 17-12. This is a parallel RLC circuit. Remember that, in this sort of situation, the resistance R should be thought of as a conductance G, with G = 1/R. Then the circuit can be called a parallel GLC circuit. At some particular frequency fo, the inductive susceptance BL will exactly cancel the capacitive susceptance BC ; that is, BL = BC. This is inevitable for some frequency fo, as long as the circuit contains finite, nonzero inductance and finite, nonzero capacitance. At the frequency fo, the susceptances cancel each other out, leaving theoretically zero susceptance. The admittance through the circuit is then very nearly equal to the conductance, G, of the resistor. If the circuit contains no resistor, but only a coil and capacitor, it is called a parallel LC circuit, and the admittance at resonance will be theoretically 0 + j0. That means the circuit will offer great opposition to alternating current at fo, and the complex impedance will theoretically be infinite! This condition is parallel resonance. In a practical parallel LC circuit, there is always a little bit of loss in the coil and capacitor, so the real part of the complex impedance is not infinite (although it can be extremely large). Calculating Resonant Frequency The formula for calculating resonant frequency fo, in terms of the inductance L in henrys and the capacitance C in farads, is as follows:
fo = 1/[2 (LC )1/2]
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