Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 34

Rayleigh-Jeans

Planck

B

Wien

λ
FIGURE 1.7 Comparison of Planck's law with its high- (Wien) and low-frequency
(Rayleigh-Jeans) approximations at 300K (from [15], courtesy of J. D. Krause, Jr.).

v

tors such as gold, silver, and copper are those in which the density of free
charges is negligible, the conduction current is proportional to the electric field
through the conductivity, and the displacement current is negligible with res-
pect to the conduction current. The propagation of an EM wave inside such a
material is governed by the diffusion equation, to which Maxwell's equations
reduce in this case. Biological materials are not good conductors. They do
conduct a current, however, because the losses can be significant: They cannot
be considered as lossless.
Solving the diffusion equation, which is valid mainly for good conductors,
where the conduction current is large with respect to the displacement current,
shows that the amplitude of the fields decays exponentially inside of the mate-
rial, with the decay parameter

1

d = m (1.48a)

12

(

wms 2

)

The parameter d is called the skin depth . It is equal to the distance within the
material at which the fields reduce to 1/2.7 (approximately 37%) of the value
they have at the interface. One main remark is that the skin depth decreases
when the frequency increases, being inversely proportional to the square root
of frequency. It also decreases when the conductivity increases: The skin depth