Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 21

microwave excitation, we shall find useful to note that the equation can be
written as

( ) ¥ ()=

f MHz l m 300 in vacuum (1.32)

Equation (1.31) shows that the wavelength is inversely proportional to the
frequency. In vacuum, the wavelength is 6000 km at 50 Hz, while it is 300 m
at 1 MHz, 0.3 m at 1 GHz, and 1 mm at 100 GHz. It also shows that the
phase velocity decreases when the relative permittivity and/or permeability
increases. It is important to observe that the phase velocity may vary signifi-
cantly from one material to the other, in particular because of the presence of
water. Water is a dielectric material with a very high dielectric constant, of the
order of 80 at low frequencies, as will be shown later. Most living tissue con-
tains a significant amount of water. As a consequence, the phase velocity at
1 GHz in a human body is almost 9 times smaller than in vacuum because the
wavelength is almost 9 times smaller than in vacuum. At higher frequency,
however, the permittivity decreases and the values of wavelength and phase
velocity are closer to their values in vacuum.
Some parameters are typical of propagation. The wave number measures
the number of wavelengths per unit length. In physicochemistry, for instance
in spectroscopy, it is still rather usual to characterize a frequency by the cor-
responding wave number. This always looks surprising to a physicist or an engi-
neer, especially when the unit length is a familiar unit rather than the meter.
As an example, a wave number of 1000 cm -1 characterizes a frequency at which
there are 1000 wavelengths over a length of 1 cm, hence with a wavelength of
1 mm, that is, in the infrared (IR).
On the other hand, the ratio of electric to magnetic field amplitudes is the
intrinsic impedance of the propagation medium. In vacuum, it is about 377 (or
120p) ohms. It is also called the wave impedance . In the nineteenth century,
the impedance of the propagation medium, in particular a vacuum, has long
been considered as puzzling. It even led some to imagine the presence of a
specific media, the ether , with no other characteristics than the permittivity and
permeability of a vacuum, offering the wave an adequate medium to propa-
gate. The wave impedance does not correspond to power absorption because
the wave can propagate in a lossless medium. This is due to the fact that, even
in the simple TEM structure, the electric field is not in phase with the mag-
netic field: Both are in quadrature, as has been said before. The wave imped-
ance expresses the ability of a propagating wave to transport power density
from one point to another in space and have it possibly absorbed there, in total
or in part. This will be explained in Section 1.4.1.
Power absorption is a very important concept when investigating biologi-
cal effects, as will be illustrated in Chapters 1-3. It is also important when
designing materials for protecting biological systems in an EM environment,
including the medical environment. Recently, EM environments have become
very complex because of the wide and rapid spread of many kinds of electric