Page 424 - Engineering Electromagnetics, 8th Edition

12 CHAPTER

Plane Wave Reflection

and Dispersion

n Chapter 11, we learned how to mathematically represent uniform plane waves
as functions of frequency, medium properties, and electric field orientation. We
Ialso learned how to calculate the wave velocity, attenuation, and power. In this
chapter we consider wave reflection and transmission at planar boundaries between
different media. Our study will allow any orientation between the wave and boundary
and will also include the important cases of multiple boundaries. We will also study
the practical case of waves that carry power over a finite band of frequencies, as
would occur, for example, in a modulated carrier. We will consider such waves in
dispersive media, in which some parameter that affects propagation (permittivity for
example) varies with frequency. The effect of a dispersive medium on a signal is of
great importance because the signal envelope will change its shape as it propagates.
As a result, detection and faithful representation of the original signal at the receiving
end become problematic. Consequently, dispersion and attenuation must both be
evaluated when establishing maximum allowable transmission distances. ■

12.1 REFLECTION OF UNIFORM PLANE
WAVES AT NORMAL INCIDENCE

We first consider the phenomenon of reflection which occurs when a uniform plane
waveisincidentontheboundarybetweenregionscomposedoftwodifferentmaterials.
The treatment is specialized to the case of normal incidence—in which the wave
propagation direction is perpendicular to the boundary. In later sections, we remove
this restriction. Expressions will be found for the wave that is reflected from the inter-
face and for that which is transmitted from one region into the other. These results are
directly related to impedance-matching problems in ordinary transmission lines, as
we have already encountered in Chapter 10. They are also applicable to waveguides,
which we will study in Chapter 13.

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