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chapt13 - CHAPTER 13 TRANSMISSION LINES Transmission lines...

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CHAPTER 13 TRANSMISSION LINES Transmission lines are used to transmit electric energy and signals from one point to another, specifically from a source to a load. This may include the connection between a transmitter and an antenna, connections between compu- ters in a network, or between a hydroelectric generating plant and a substation several hundred miles away. Other familiar examples include the interconnects between components of a stereo system, and the connection between a cable service provider and your television set. Examples that are less familiar include the connections between devices on a circuit board that are designed to operate at high frequencies. What all of the above examples have in common is that the devices to be connected are separated by distances on the order of a wavelength or much larger, whereas in basic circuit analysis methods, connections between elements are of negligible length. The latter condition enabled us, for example, to take for granted that the voltage across a resistor on one side of a circuit was exactly in phase with the voltage source on the other side, or, more generally, that the time measured at the source location is precisely the same time as measured at all other points in the circuit. When distances are sufficiently large between source and receiver, time delay effects become appreciable, leading to the delay-induced phase differences mentioned above. In short, we deal with wave phenomena on transmission lines, just as we did with point-to-point energy propagation in free space or in dielectrics. The basic elements in a circuit, such as resistors, capacitors, inductors, and the connections between them, are considered lumped elements if the time delay 435
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in traversing the elements is negligible. On the other hand, if the elements or interconnections are large enough, it may be necessary to consider them as distributed elements. This means that their resistive, capacitive, and inductive characteristics must be evaluated on a per-unit-distance basis. Transmission lines have this property in general, and thus become circuit elements in them- selves, possessing impedances that contribute to the circuit problem. The basic rule is that one must consider elements as distributed if the propagation delay across the element dimension is on the order of the shortest time interval of interest. In the time-harmonic case, this condition would lead to a measurable phase difference between each end of the device in question. In this chapter, we investigate wave phenomena in transmission lines, in ways that are very similar to those used in the previous two chapters. Our objectives include (1) to understand how to treat transmission lines as circuit elements possessing complex impedances that are functions of line length and frequency, (2) to understand the properties of different types of lines, (3) to learn methods of combining different transmission lines to accomplish a desired objec- tive, and (4) to understand transient phenomena on lines.
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