ELECTRICAL PROPERTIES OF DIELECTRICS - Advanced Signal Integrity for High-Speed Digital Design - page 254

6.2 CLASSIFICATION OF DIELECTRIC MATERIALS

In Section 5.1.1 it was shown that when a plane wave propagates in a conductive
medium such as a metal, Ampere's law reduces to

= jω ε − j σ
ω

E

∇× H (6-14)

In the case of a conductor, which was the topic of Chapter 5, the conductivity
term σ represented the metal losses. Conductivity implies the movement of free
charges within a material. In the case of a good dielectric, the charges are bound.
However, as discussed in Section 6.1, the interaction between the molecular
or atomic structure of the dielectric and the applied electric field changes the
orientation of the bound charges within the material. As an example, equation
(6-1) calculated the force required to displace the electron cloud of an atom.
Consequently, as the electric dipoles within a material attempt to remain aligned
with the time-varying electric field, energy is consumed, which manifests itself
as dielectric losses. Subsequently, the term σ in (6-14) can be thought of as the
equivalent conductivity of the dielectric, which represents the losses due to the
polarization of the material. This allows the definition of the complex permittivity
for a lossy dielectric, as was done for conductors in Chapter 5:

ε = ε − j σ dielectric
ω

= ε − jε (6-15)

The imaginary portion of the complex dielectric permittivity represents the dielec-
tric losses, and the real portion represents the dielectric permittivity ε = ε r ε 0 ,
discussed throughout this topic. For most practical purposes, materials are clas-
sified by the real part of (6-15) divided by the permittivity of free space:

ε
ε 0

ε r = (6-16a)

which is known as the relative dielectric permittivity, and the loss tangent,

ε
ε

tan | δ |= (6-16b)

which is simply the ratio of the imaginary and real components of (6-15).

6.3 FREQUENCY-DEPENDENT DIELECTRIC BEHAVIOR

In Section 6.1 we showed that when a dielectric is subjected to an external elec-
tric field, the positive and negative charges bound to the atoms and molecules
are displaced relative to their average positions, causing electric dipoles to be
formed which are quantified using the polarization vector

P . Furthermore, the