Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 7

particular conductors, semiconductors, and superconductors. Classical physics
almost completely fails when trying to establish quantitative models. It can
however yield some very illuminating insight on the phenomena involved with
the dielectric character of materials, in particular about the influence of fre-
quency, as will be shown now.
The dipolar polarization , resulting from the alignment of the molecule
dipolar moment due to an applied field, is a rather slow phenomenon. It is cor-
rectly described by a first-order equation, called after Debye [5]: The dipolar
polarization reaches its saturation value only after some time, measured by a
time constant called relaxation time t . The ability to polarize, called the polar-
izability , is measured by the parameter

a

0

a = + C (1.7)

d

1 + j wt

where constant C takes into account the nonzero value of the polarizability at
infinite frequency. The relative permittivity related to this phenomenon is

ee e
r

=¢- ¢ j (1.8)

r r

where N is the number of dipoles per unit volume. It should be observed that
the permittivity is a complex quantity with real and imaginary parts. If e r 0 and
e r • are the values of the real part of the relative permittivity at frequencies
zero and infinity, respectively, one can easily verify that the equations can be
written as

( ) ee

wt

- ee - t

r 0 r • r 0 r •

(1.9)

e ¢= + e e ¢¢ =

r r • r

1 +

22

1 + wt

22

The parameter e r • is in most cases the value at optical frequencies. It is often
called the optical dielectric constant .
Dipolar polarization is dominant in the case of water, much present on
earth and an essential element of living systems. The relative permittivity of
water at 0°C is

83

e r =+ + 5 (1.10)

( ) 1 j 0 113 . f z

with 1/t = 8.84 GHz. The real part of the relative permittivity is usually called
the dielectric constant , while the imaginary part is a measure of the dielectric
losses. These are often expressed also as the tangent of the loss angle :

e
e

¢¢
¢

tan d =

e

(1.11)

Table 1.1 shows values of relaxation times for several materials. A high value
of the relaxation time is indicative of a good insulator, while small values are
typical of good conductors.