Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 43

itly: Any material with a single relaxation time, characterized by e s and e • ,
gives the same plot. Hence, in reporting results, it is essential to supply the
magnitude of t in addition to the plot. The power at which wt appears in Eqn.
(1.7) is not always unity. When it is smaller than unity, the plot represents only
an upper portion of a semicircle.
When the steady conductivity contributes significantly to e≤ ( w ) , the repre-
sentation of dielectric data is affected in the Cole-Cole plot [5]. The presence
of several relaxation times also complicates the representation. In view of this,
Fröhlich has introduced a distribution function in which the relaxation time
depends on the (absolute) temperature, and he assumes that the polarizable
units are evenly distributed in terms of activation energy [21]. There is no
reason why activation energies should be evenly distributed over a small
range of values while higher or lower values should be absent. Fröhlich's dis-
tribution can be generalized by assuming that most activation energies have
a median value while deviant values are increasingly unlikely, yielding some
sort of a Gaussian distribution of activation energies [5].
However, Cole and Cole designed a function that is not very different in
practice from a Gaussian distribution. It is a useful representation for many
experimental results, and this seems reasonable in view of its similarity to
a Gaussian distribution. Several other distribution functions were designed
later.

1.7 DIELECTRIC MEASUREMENTS

Accurate knowledge of the complex relative permittivity of biological tissues
is necessary to evaluate biological effects as well as the efficiency of medical
applications. There are a variety of measurement methods, based however on
a rather limited number of principles.

1.7.1 RF Measurements

The complex permittivity—dielectric constant and losses—of a material is
almost always measured by inserting a specimen into a capacitor, waveguide,
or cavity which forms part of an electrical circuit. The circuit is subject to an
alternating voltage or wave or to step functions. Above 1 MHz, however, which
covers the RF/microwave range, the source delivers most generally a CW. In
all cases, errors may arise if effects due to some part of the external circuit are
ascribed to the specimen. It is extremely important to point out the limits of
experimental accuracy. Furthermore, some sources of error might escape the
experimenter when using ready-made equipment.
For frequencies higher than a few megahertz, representation of a circuit by
discrete circuit elements and by wires free of inductance and capacitance
becomes gradually unrealistic. For higher frequencies, circuits are considered
as distributed impedances, and the specimen is incorporated accordingly.