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PROBLEMS

3.1. A plane wave at 30 GHz is incident at a right angle upon the skin (e =
18 - j 19).
(a) Find the reflection coefficient G.
(b) Show that the SAR is given by SAR(0) e - 2x /d , where

( )

21 2

p - G

inc

()=

SAR 0

d

r
is the mass density of skin, and d is the penetration depth in skin.
Assume that the skin has a density of 1000 kg/m 3 .
(c) Plot the SAR as a function of depth for p inc = 10 mW cm -2 .
3.2. Assume that the monopole of problem 1.13 is fed by a 33 W coaxial cable.
(a) Find the available power of a source feeding the cable if the cable is
lossless, and the monopole terminal voltage is 0.5 V.
(b) A numerical analysis of the equivalent dipole antenna with V 0 = 1V
has provided an SAR profile in the medium as given by the follow-
ing table 1 .
If 2 W of power is available through the coaxial cable, calculate the tempera-
ture rise at r = 5 mm, for axial distances z = 5, 15, and 20 mm, when the power

is the SAR at the interface, p inc is the incident power per unit area,

1 J. P. Casey, R. Bansal, “The near field of an insulated dipole in a dissipative dielectric medium,”
IEEE Trans. Microwave Theory Tech. , Vol. MTT-34, No. 4, pp. 459-463, Apr. 1986.