Biomedical Engineering Reference
In-Depth Information
1.4.
The electric field intensity of the plane wave inside medium 1 of problem
1.3 is given by
E
=
E
01
e
-g
z
+G
E
01
e
g
z
. The first term characterizes the wave
propagating in the +
z
direction, and the second term characterizes the
wave propagating in the -
z
direction. The interface determining the
reflection coefficient G is located at
z
= 0. Show that the absorbed power
in the unit volume is
1
[
]
P
=
(
s
Ee
)
+
r
e
+
2
r
cos
(
2
b
z
+
j
)
+
-
2
a
z
2
2
a
z
2
01
1.5.
Assume that a wave with
E
0
(
z
= 0
-
) = 200 V m
-1
is propagating in the
z
direction inside a fat medium and is incident upon a semi-infinite muscle
medium that fills
z
> 0.
(a)
Write explicit relations for the power absorbed per unit volume
P
in both media at 915 MHz, 2.45 GHz, and 10 GHz, respectively.
(b)
Plot the values of power absorbed as a function of
z
(-0.1 m <
z
).
1.6.
Repeat problem 1.5 for power absorbed in medium 2, assuming that
medium 1 is air and medium 2 is skin. Assume that the skin is thick
enough to ensure there is no reflecting wave present in it. Plot the results
for 0 <
z
< 0.003 m.
1.7.
In multilayered cases, the reflection coefficient at the interface of
mediums
i
and
i
+ 1 is
i
- 1
i
i
+ 1
(
)
(
)
G
i
=
Z
-
Z
Z
+
Z
(
)
(
)
in
i
+
1
0
i
in
i
+
1
0
i
where
Z
0
i
= 120p
/(
e
0
e
i
)
1/2
z
and
1
1
+
-
G
G
e
e
-
2
g
d
1
++
il
1
(
i
+
1
)
Z
=
Z
(
)
(
)
in
i
+
1
0
i
+
1
-
2
g
d
1
++
il
1
(
i
+
1
)
z
=
z
l
+1
z
=
z
i
is the input impedance of medium
i
+ 1 seen in this boundary, with
d
i
being the thickness of medium
i
. Assume that a wave at 915 MHz and
E
+
= 1 V/m is propagating in air (
i
= 1) and is incident upon three layers
of skin (
d
2
= 1 mm), fat (
d
3
= 5 mm), and muscle (
d
4
=•).
(a)
Find the reflection coefficient at each interface.
(b)
Find the electric field intensity and absorbed power at the two sides
of each interface and 10 mm into the muscle. Note that the electric
field inside medium
i
can be written as
E
i
+G
i
E
0
i
e
+g
i
(
z
-
z
i
)
,
where
E
0
i
is the electric field in the +
z
direction wave at
z
=
z
i
.
(c)
Plot the profile of the absorbed power as a function of the penetra-
tion into these media.
=
E
0
i
e
-g
i
(
z
-
z
i
)
1.8.
Repeat problem 1.7 for
f
= 2.45 GHz and comment on the results.
1.9.
Repeat problem 1.7 for
f
= 10 GHz and comment on the results.
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