ELECTROMAGNETIC FUNDAMENTALS FOR SIGNAL INTEGRITY - Advanced Signal Integrity for High-Speed Digital Design - page 10

2.7.1 Plane wave incident on a perfect conductor 57

2.7.2 Plane wave incident on a lossless dielectric 60

References 62

Problems 62

Much of signal integrity is based heavily in electromagnetic theory. Various
aspects of this theory are found in numerous topics on a variety of topics, such
as microwaves, electromagnetics, optics, and mathematics. To rely on these topics
to form a basis of the fundamental understanding of signal integrity would result
in a confusing disarray of conflicting assumptions, notations, and conventions.
Although it is assumed that readers have a basic understanding of electromag-
netics, the presentation of Maxwell's equations and subsequent solutions in the
form most often used in signal integrity will minimize confusion and help readers
extract the relevance from the haze of mathematical calculation often encountered
in generalized electromagnetic textbooks. It is also convenient to summarize, in
one place, the underlying physics that forms the basis of succeeding chapters. In
this section we present Maxwell's equations and the underlying electromagnetic
theory needed for signal integrity. The concepts are used and expanded on in
several subsequent chapters. This analysis does not constitute a complete theo-
retical study; however, it does present the fundamental electromagnetic concepts
needed to develop the basis of signal integrity theory. As the topic progresses,
this material will be built on to describe more advanced concepts as they are
applied to real-world examples.
Initially, the most common vector operators are reviewed briefly. This is
important because Maxwell's equations will be presented in differential form
and a fundamental understanding of the vector operators will allow readers to
visualize the behavior of electromagnetic fields. Next, the equations that gov-
ern a plane wave propagating in free space are derived directly from Maxwell's
equations. Then the concepts of wave propagation, intrinsic impedance, and the
speed of light are derived. Next, the theory of electrostatics and magnetostatics
is covered to explain the physical meaning of an electric and a magnetic field,
the energy they contain, and how they relate to specific circuit elements, such
as inductance and capacitance, used in later chapters. Finally, we discuss the
power carried by electromagnetic waves and how they react when propagating
into different materials, such as metal or other dielectric regions. Other aspects of
electromagnetic theory are covered in later chapters, but the basis of that analysis
is defined here.

2.1 MAXWELL'S EQUATIONS

Electromagnetic theory is described by Maxwell's equations, published originally
in 1873. In this section we outline the fundamentals of electromagnetic theory