Basic Physical Principles - Broadband Reflectometry for Enhanced Diagnostics and Monitoring Applications - page 20

chapters, for microwave reflectometry-based dielectric spectroscopy of materials,
either the direct frequency domain (FD) approach or the time domain/frequency
domain (TD/FD) combined approach can be adopted [28].

2.4.1 Dielectric Relaxation Models

Materials can be classified according to their dielectric permittivity. The dielectric
behavior of a material is suitably described by the frequency-dependent complex
relative permittivity, ε r ( f ) , which can be written as follows [4]:

i

σ 0

ε r ( )= ε r ( ε

r

f f ) − ( f )+ (2.33)

2 π f ε 0

ε 0 = where i 2 10 − 12 Fm − 1 is the dielectric permittivity of free space, = − 1, 8 . 854 ×

ε r ( ε

r

f is the frequency, f ) describes energy storage, ( f ) accounts for the dielec-

tric losses, and σ 0 is the static electrical conductivity (which is related to the ionic

losses). Generally, when

ε r ) >>

( σ 0 / 2 π f 1, the material can be considered a good

ε r ) << conductor. On the other hand, when 1, the material is considered a

dielectric (i.e., lossless or low-loss material). Materials with a large amount of loss
inhibit the propagation of electromagnetic waves. Those that do not fall under either
limit are considered to be general media. A perfect dielectric is a material that has
no conductivity, thus exhibiting only a displacement current.
The dielectric relaxation refers to the relaxation response of a dielectric medium
to an external electric field of microwave frequencies. This relaxation is often de-
scribed, in terms of dielectric permittivity, through the so-called relaxation models .
Fig. 2.8 shows a schematization of typical relaxation phenomena.
There are several mathematical models (obtained either theoretically or empiri-
cally) that are used to describe the dielectric properties of materials.
For example, for pure polar materials, the equation known as Debye model de-
scribes the dielectric permittivity [9]:

( σ 0 / 2 π f

Fig. 2.8 Generic dielectric
permittivity spectrum over a
wide range of frequencies.
The figure shows the main
processes that occur: ionic
and dipolar relaxation, and
atomic and electronic res-
onances at higher energies
[1]