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Fundamentals of Electromagnetics CHAPTER ONE
Fundamentals of
Electromagnetics
1.1 RF AND MICROWAVE FREQUENCY RANGES
The rapid technological advances in electronics, electro-optics, and computer
science have profoundly affected our everyday lives. They have also set the
stage for an unprecedented drive toward the improvement of existing medical
devices and the development of new ones. In particular, the advances in radio-
frequency (RF)/microwave technology and computation techniques, among
others, have paved the way for exciting new therapeutic and diagnostic
methods. Frequencies, from RF as low as 400 kHz through microwave fre-
quencies as high as 10 GHz, are presently being investigated for therapeutic
applications in areas such as cardiology, urology, surgery, ophthalmology,
cancer therapy, and others and for diagnostic applications in cancer detection,
organ imaging, and more.
At the same time, safety concerns regarding the biological effects of
electromagnetic (EM) radiation have been raised, in particular at a low level
of exposure. A variety of waves and signals have to be considered, from pure
or almost pure sine waves to digital signals, such as in digital radio, digital
television, and digital mobile phone systems. The eld has become rather
sophisticated, and establishing safety recommendations or rules and making
adequate measurements require quite an expertise.
In this book, we limit ourselves to the effects and applications of RF and
microwave elds. This covers a frequency range from about 100 kHz to 10 GHz
and above. This choice is appropriate, although effects at RF and microwaves,
RF/Microwave Interaction with Biological Tissues, By André Vander Vorst, Arye Rosen, and
Youji Kotsuka
Copyright © 2006 by John Wiley & Sons, Inc.
7 8
FUNDAMENTALS OF ELECTROMAGNETICS
respectively, are of a different nature. It excludes low-frequency (LF) and
extremely low frequency (ELF) effects, which do not involve any radiation. It
also excludes ultraviolet (UV) and X-rays, called ionizing because they can
disrupt molecular or atom structures. The RF/microwave frequency range
covered here may be called nonionizing.
Radiation is a phenomenon characterizing the RF/microwave range. It is
well known that structures radiate poorly when they are small with respect to
the wavelength. For example, the wavelengths at the power distribution fre-
quencies of 50 and 60 Hz are 6.000 and 5.000 km, respectively, which are enor-
mous with respect to the objects we use in our day-to-day life. In fact, to radiate
efciently, a structure has to be large enough with respect to the wavelength
l. The concepts of radiation, antennas, far eld, and near eld have to be
investigated.
On the other hand, at RF and microwave frequencies, the electric (E) and
magnetic (H) elds are simultaneously present: if there is an electric eld, then
there is a coupled magnetic eld and vice versa. If one is known, the other can
be calculated: They are linked together by the well-known Maxwells equa-
tions. Later in this book, we shall be able to separate some biological effects
due to one eld from some due to the other eld.We need, however, to remem-
ber that we are considering the general case, which is that of the complete
eld, called the EM eld. Hence, we are not considering direct-current (DC)
and LF electric or magnetic elds into tissue.
Because we limit ourselves to the RF/microwave range, we may refer to our
subject of interaction of electric and magnetic elds with organic matter as
biological effects of nonionizing radiation. It should be well noticed that, by
specically considering a frequency range, we decide to describe the phenom-
ena in what is called the frequency domain, that is, when the materials and
systems of interest are submitted to a source of sinusoidal elds. To investigate
properties over a frequency range, wide or narrow, we need to change the
frequency of the source. The frequency domain is not physical because a
sinusoidal source is not physical: It started to exist an innite amount of time
ago and it lasts forever. Furthermore, the general description in the frequency
domain implies complex quantities, with a real and an imaginary part, res-
pectively, which are not physical either. The frequency-domain description is,
however, extremely useful because many sources are (almost) monochromatic.
To investigate the actual effect of physical sources, however, one has to
operate in what is called the time domain, where the phenomena are described
as a function of time and hence they are real and physically measurable. Oper-
ating in the time domain may be rather difcult with respect to the frequency
domain. The interaction of RF/microwave elds with biological tissues is inves-
tigated mostly in the frequency domain, with sources considered as sinusoidal.
Today numerical signals, such as for telephony, television, and frequency-
modulated (FM) radio, may, however, necessitate time-domain analyses and
measurements. FIELDS
9
There is an interesting feature to note about microwaves: They cover,
indeed, the frequency range where the wavelength is of the order of the size
of objects of common use, that is, meter, decimeter, centimeter, and millime-
ter, depending of course on the material in which it is measured. One may,
hence, wonder whether such wavelengths can excite resonance in biological
tissues and systems. We shall come back later to this question.
1.2 FIELDS
Investigating the interaction of EM elds with biological tissues requires
a good physical insight and mathematical understanding of what are
elds. A eld is associated with a physical phenomenon present in a given
region of space. As an example, the temperature in a room is a eld
of temperature, composed of the values of temperature in a number of
points of the room. One may say the same about the temperature distribution
inside a human body, for instance. We do not see the eld, but it exists,
and we can for instance visualize constant-temperature or isothermal
surfaces.
There are elds of different nature. First, elds may be either static or time
dependent. Considering, for instance, the temperature eld just described, the
room may indeed be heated or cooled, which makes the temperature eld time
dependent. The human body may also be submitted to a variety of external
sources or internal reasons which affect the temperature distribution inside
the body. In this case, the isothermal surfaces will change their shapes as a
function of time.
Second, the nature of the eld may be such that one parameter only, such
as magnitude, is associated with it. Then, the eld is dened as scalar. The tem-
perature eld, for instance, inside a room or a human body, is a scalar eld.
One realizes that plotting a eld may require skill, and also memory space, if
the structure is described in detail or if the observer requires a detailed
description of the eld in space. This is true even in the simplest cases, when
the eld is scalar and static.
On the other hand, in a vector eld, a vector represents both the
magnitude and the direction of the physical quantity of interest at points in
space, and this vector eld may also be static or time dependent. When
plotting a static scalar eld, that is, one quantity, in points of space already
requires some visualization effort. On the other hand, plotting a time-
dependent vector eld, that is, three time-varying quantities, in points of space
obviously requires much more attention. A vector eld is described by a set
of direction lines, also known as stream lines or ux lines. The direction line is
a curve constructed so that the eld is tangential to the curve in all points of
the curve. 10
FUNDAMENTALS OF ELECTROMAGNETICS
1.3 ELECTROMAGNETICS
1.3.1 Electric Field and Flux Density
The electric eld E is derived from Coulombs law, which expresses the inter-
action between two electric point charges. Experimentally, it has been shown
that
1. Two charges of opposite polarity attract each other, while they repel
when they have the same polarity, and hence a charge creates a eld of
force.
2. The force is proportional to the product of charges.
3. The force acts along the line joining the charges and hence the force eld
is vectorial.
4. The force is higher when the charges are closer.
5. The force depends upon the electric properties of the medium in which
the charges are placed.
The rst observations showed that the force is about proportional to the
square of the distance between them. In 1936, the difference between the mea-
sured value and the value 2 for the exponent was of the order of 2 ¥ 10
-9
[1]. It is admitted as a postulate that the exponent of the distance in the law
expressing the force between the two charges is exactly equal to 2. It has been
demonstrated that this postulate is necessary for deriving Maxwells equations
from a relativistic transformation of Coulombs law under the assumption that
the speed of l