Biomedical Engineering Reference
In-Depth Information
s
we
j
Ê
Ë
ˆ
¯
ee
=¢ -¢¢
e e
(
j
e
)
=¢ -
e e
=¢
ee
(
1
-
j
tan
d
)
0
0
0
0
0
In this relation, e
0
= 8.854 ¥ 10
-12
Fm
-1
and s and tand
(
= s
/
we
0
e≤
)
are the
conductivity and the loss tangent of the medium, respectively.
(a)
Prove the following expressions:
we
¢
a
=
-
1
Np m
1
+
tan
d
-
1
2
c
2
we
¢
rad
m
b
=
+
1
1
+
tan
d
-
1
2
c
2
Hint
: Calculate g
2
, which yields b
2
- a
2
and ab.
(b)
Show that the wavelength (=
2
p
/
b) is
-
1
e
¢
Ê
Ë
ˆ
¯
ll
=
+
1
m
1
+
tan
d
2
0
2
1.2.
The complex permittivity of skin, fat, and muscle at 915 MHz, 2.45 GHz,
and 10 GHz, respectively, is given in the following table:
915 MHz
2.45 GHz
10 GHz
e¢
e≤
e¢
e≤
e¢
e≤
Skin
41.5
17
38
11
31
14.5
Fat
11.3
2.2
10.9
2
8.8
3.1
Muscle
55
19
53
12.5
43
19
(a)
Calculate the loss tangent and the parameters a, b, and l for these
media at the specified frequencies.
(b)
The penetration depth d is the inverse of the attenuation constant
a. Find d for these media at the specified frequencies.
1.3.
A plane wave is incident from semi-infinite medium 1 to semi-infinite
medium 2 and propagates normal to the boundary between the two
media. The reflection coefficient of a plane wave with normal incidence
on a flat boundary is given as
2
1
e
-
+
e
1
2
G=
r
e
j
j
=
Z
e
e
1
2
Z
= 0
where r and j are the magnitude and phase of the reflection coefficient,
respectively. Find the reflection coefficients of the air-skin, skin-fat, and
fat-muscle interfaces at the specified frequencies of problem 1.2.
Search WWH ::
Custom Search