Biomedical Engineering Reference
In-Depth Information
designate the mean incident angle and reflected angle at the
surface of a conductive plate in medium II, respectively, satisfying the relation
q
i
¢=q
r
¢=q
t
. We imposing the following boundary conditions to expressions
(5.1)-(5.4):
where q
i
¢
and q¢
In
z
=
0:
HH
x
=
(5.5)
1
x
2
z
=
0
z
=
0
E
=
E
(5.6)
y
1
y
2
z
=
0
z
=
0
In
z
=
d:
E
y
=
0
(5.7)
2
z
=
d
Then we obtain the expression of the reflection coefficient:
Z
Z
-
+
1
1
cos
cos
q
TE
t
S
=
(5.8)
q
TE
i
where
m
em
2
p
l
Ê
Ë
ˆ
¯
r
2
Z
=
tanh
j
em
-
sin
2
q
d
(5.9)
TE
r
22
r
i
-
sin
q
r
22
r
i
and where e
r
and m
r
are the relative permittivity and relative permeability,
respectively. The reflection coefficient
S
=
B/A
. In the course of this deriva-
tion, Snell's law has been used:
sin
sin
q
g
g
t
i
=
1
q
2
In the case of normal incidence of the TE wave, we can obtain the reflection
coefficient by putting q
i
=
0. Then,
[
]
-
me
tanh
tanh
j
(
2
plem
)
d
1
S
=
r
2
r
2
r
2
r
2
(5.10)
[
]
+
(
)
me
j
2
plem
d
1
r
2
r
2
r
2
r
2
Similarly, we can derive the reflection coefficient for a TM wave:
Z
Z
-
+
cos
cos
q
TM
i
S
=
(5.11)
q
TM
i
where
em
-
sin
q
2
p
l
d
2
Ê
Ë
ˆ
¯
r
22
r
i
Z
=
tanh
j
em
-
sin
2
q
(5.12)
TM
r
22
r
2
e
r
2
Search WWH ::
Custom Search