Wave Propagation in Linear Media | re-examined

Chapter 3
Wave propagation in
electromagnetic transmission lines
One cannot escape the feeling that these mathematical formulae have an
independent existence of their own, that they are wiser than we are, wiser
even than their discoverers, that we get more out of them than was originally
put into them. Heinrich Hertz, quoted in [1]
As the historical review shows, opinions are divided on the question of wave propagation.
To gain some further insight, we shall explore several examples in the sequel, ranging from
the simple case of a homogeneous transmission line to transient phenomena in wave guides.
The main interest of the analysis lies on signals in the evanescent region or stop band of
transmission lines, and among the many de nitions of the propagation velocity, we shall
concentrate on that of energy velocity. Not only is its de nition clear-cut and intuitive, we
shall also nd that it gives reasonable results where the concept of group velocity must fail.
At the beginning of the chapter, we study the homogeneous and lossless transmission line
in the pass band and con rm the equality of group and energy velocity. We then digress
to explore a classical delay line known from the literature, where this identity also holds.
Gradually complicating the model, we consider evanescence in connection with a mismatched
termination of a nitely long transmission line. The logical extension of this investigation is to
consider a frequency-dependent medium. We thus evaluate the behaviour of waves in a lossless
plasma. A short section on an inhomogeneous transmission line concludes the treatment of
monochromatic signals. A large part is then devoted to the evaluation of transients in a
plasma and a rectangular wave guide. In both cases we shall encounter the propagation of a
wave front, whose velocity will be equal to the velocity of light. The remainder of the chapter
explores the propagation of a Gaussian pulse in plasma. In connection with this comparatively
small-band signal, we shall also touch upon the question of causality inevanescent media.
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