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Chapter 1
Radio Wave Fundamentals
Radio wave propagation is governed by the theory of electromagnetism laid down by the Scottish physicist and mathematician James Clerk Maxwell (13 June 1831 to 5 November 1879) who demonstrated that electricity, magnetism and light are all manifestations of the same phenomenon. Electromagnetic wave propagation depends on the properties of the transmission medium in which they travel. Classifications of transmission media include linear versus nonlinear, bounded versus unbounded, homogeneous versus nonhomogeneous and isotropic versus nonisotropic. Linearity implies that the principle of superposition can be applied at a particular point, whereas a medium can be considered bounded if it is finite in extent or unbounded otherwise. Homogeneity refers to the uniformity of the physical properties of the medium at different points and an isotropic medium has the same physical properties in different directions.
In this chapter we start by a revision of the fundamentals of Maxwell's wave equations and polarization. This is followed by a discussion of the different propagation phenomena including reflection, refraction, scattering, diffraction, ducting and frequency dispersion. These are discussed in relation to different transmission media such as propagation in free space, the troposphere and the ionosphere. For a more detailed treatment of the subject, the reader is referred to [1, 2].
1.1 Maxwell's Equations
Originally Maxwell's equations referred to a set of eight equations published by Maxwell in 1865. In 1884 Oliver Heaviside, concurrently with other work by Willard Gibbs and Heinrich Hertz, modified four of these equations, which were grouped together and are nowadays referred to as Maxwell's equations. Individually, these four equations are known as Gauss's law, Gauss's law for magnetism, Faraday's law of induction and Ampere's law with Maxwell's correction.
Fundamental to Maxwell's four field equations is the differential vector operator
(pronounced
del) and the bold denotes a vector given by:
For a scalar V and a vector function A with components along the xyz axes:
there are three possible operations related to the
operator, defined as follows:
1. The gradient of a scalar V is a vector given by:
2. The divergence of
is a scalar given by:
3. The curl of
is a vector given by:
or
Related to these operators are the following identities:
where
Using the
operator, Maxwell's four equations relate the electric field
E volts per m (V/m) and magnetic field
H amperes per metre (A/m), as given in Equations (
1.11 to
1.14):
where ρ is the charge density in coulombs per cubi...
