Page 319 - Engineering Electromagnetics, 8th Edition

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CHAPTER

Transmission Lines

ransmission lines are used to transmit electric energy and signals from one
point to another, specifically from a source to a load. Examples include the
T connection between a transmitter and an antenna, connections between com-
puters in a network, or connections between a hydroelectric generating plant and a
substation several hundred miles away. Other familiar examples include the intercon-
nects 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 these 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 assumed to have
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 delay-induced phase differences. In short, we
deal with wave phenomena on transmission lines in the same manner that we deal
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 in
traversing the elements is negligible. On the other hand, if the elements or inter-
connections 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 prop-
erty in general, and thus they become circuit elements in themselves, 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 dimen-
sion is on the order of the shortest time interval of interest. In the time-harmonic case,

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