Biomedical Engineering Reference
In-Depth Information
2
p
l
Ê
Ë
ˆ
¯
ZZ
=
tanh
g
dZ
=
tanh
j
em
d
(5.16)
N
CN
N
N
CN
rN
rN
Since the impedance looking into the
n
th layer at the surface of the
n
th layer
is denoted by
Z
n
,
Z
n
-1
is expressed by the following recurrence formula using
the intrinsic impedance
Z
cn
in the
n
th layer:
ZZ
ZZ
+
tanh
tanh
g
d
=
n
cn
-
1
n
-
1
n
-
1
(5.17)
n
-
1
cn
ZZ
+
g
d
cn
-
1
n
n
-
1
n
-
1
Note that this recurrence formula should be calculated from the side of a ter-
minal conductive plate. Then, calculating
Z
n
successively from the impedance
Z
N
looking into the
N
th layer, we can obtain the value of
Z
1
. Hence, the reflec-
tion coefficient
S
is obtained by substituting the free-space impedance
Z
0
and
Z
1
in expression (5.15).
Oblique Incident Case
The recurrence formula (5.17) can be used also when
the plane wave with an incident angle
is obliquely transmitted to the multi-
player-type wave absorber. However, the equations which calculate the input
impedance
Z
cn
, propagation constant g
n
, and reflection coefficient
S
of the
n
th
layer differ from the previous case, such as the following equations, depend-
ing on the TE wave or TM wave:
q
1. TE wave:
m
em
Z
0
rn
Z
=
(5.18)
cn
-
sin
q
2
r n
rn
2
p
l
g
=
j
em
-
sin
q
2
(5.19)
n
r n
r n
ZZ
ZZ
-
+
cos
cos
q
1
0
S
=
(5.20)
TE
q
1
0
2. TM wave:
Z
em
-
sin
2
q
Z
=
0
rn
rn
(5.21)
cn
e
rn
2
p
l
g
=
j
em
-
sin
q
2
(5.22)
n
r n
r n
ZZ
ZZ
-
+
cos
cos
q
1
0
S
=
(5.23)
TM
q
1
0
The reflection coefficient can be calculated from Eqns. (5.20) and (5.23) if the
recurrence formula (5.17) is calculated using the values of
Z
cn
and g
n
in each
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